Algebra 1
an integer that indicates how many times a root is multiplied by itself to equal a radicand = ³ √
(263) index (Unit 8: Exponential & Radical Functions - Lesson 4: Radical Expressions)
(155) Quotient of Powers Property Quo-of-Pows-Prop) (Unit 5: Exponents and Polynomials - Lesson 3: Multiplication & Division Properties of Exponents)
A power divided by another power with the same base is equal to the base raised to the difference of the exponents. If a ≠ 0 and m & n are integers, then (Quo-of-Pows-Prop):
(152) Product of Powers Property Prod-Pow-Prop (Unit 5: Exponents and Polynomials - Lesson 3: Multiplication & Division Properties of Exponents)
A power multiplied by another power with the same base is equal to the base raised to the sum of the exponents. If a ≠ 0 and m & n are integers, then (Prod-Pow-Prop):
(153) Power of a Power Property Pow-ofa-Pow-Prop (Unit 5: Exponents and Polynomials - Lesson 3: Multiplication & Division Properties of Exponents)
A power raised to another power is equal to the base raised to the product of the exponents. If a ≠ 0 and m & n are integers, then (Pow-ofa-Pow-Prop):
(156) Positive Power of a Quotient Property +ve-Pow-ofa-Quo-Prop (Unit 5: Exponents and Polynomials - Lesson 3: Multiplication & Division Properties of Exponents)
A quotient raised to a positive power is equal to the quotient of each base raised to that power. If a ≠ 0 and m & n are integers, then (+ve-Pow-ofa-Quo-Prop):
(197) Zero Product Property (Unit 6: Quadratic Functions - Lesson 7: Solving Quadratic Equations by Factoring)
If the product of two factors equals zero, then at least one of the factors must equal zero. if ab=0, then a=0 or b=0
(165) not monomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
Non whole numbers, like negative exponents, exponents in denominator, or not single terms / they are the sum or difference of terms
(268) TABLE OF COMMON POWERS (8.4.1) (Unit 8: Exponential & Radical Functions - Lesson 4: Radical Expressions)
Table 8.4.1 of Common Powers
(54) constant (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
a value that does not change
(124) parent function (Unit 3: Inequalities & Linear Functions - Lesson 10: Transformations in Linear Functions)
the most basic function of a family of functions
(34) numerator (Unit 1: Pre-Test Skills - Skill 11: Writing Fractions in Simplest Terms)
the top number in a fraction that shows the number of equal parts being considered
(173) factor (Unit 5: Exponents and Polynomials - Lesson 8: Factoring Polynomials)
to express a value as a product of two or more factors
(77) solve an equation (Unit 2: Expressions, Functions, & Equations - Lesson 5: Solving Equations With Addition & Subtraction)
to find the set of values that makes the equation true
(199) solve slope from 2 points (Unit 6: Quadratic Functions - Lesson 8: Solving Quadratic Equations by Using Square Roots)
to find the slope of the line using two points. eg. (1, 3),(2, 5) m = 5 - 3 = 2 =2 ....... 2 - 1..... 1
(134) coincide (Unit 4: Systems of Equations & Inequalities - Lesson 6: Special Systems)
to occupy the same space at the same time; lines that coincide are coincident
(75) isolate the variable (Unit 2: Expressions, Functions, & Equations - Lesson 5: Solving Equations With Addition & Subtraction)
to perform whatever operations are necessary so that the variable appears by itself on one side of the equation but not on the other side
(23) prime numbers (Unit 1: Pre-Test Skills - Skill 6: Prime & Composite Numbers & Prime Factorization)
whole numbers with only two factors—themselves and 1
(131) 3 Limitations of Graphing (Unit 4: Systems of Equations & Inequalities - Lesson 3: Limitations of Graphing)
- 1 - If you are not careful to plot straight, accurate lines, the point of intersection will be incorrect. If the point of intersection is incorrect, the solution to the problem will be wrong and the ordered pair you find will not satisfy both equations. - 2 - If the lines intersect at a shallow angle, the point of intersection will be difficult, if not impossible, to determine. - 3 - The graphing method does not work well when solving systems of linear equations that contain coordinates with fractions or decimals.
(141) system of linear inequalities (Unit 4: Systems of Equations & Inequalities - Lesson 8: Systems of Linear Inequalities)
- a set of 2 or more linear inequalities considered together - The solution for a system of linear inequalities must satisfy the conditions of both inequalities in the system in order for the solution to be true. - When graphing a system of linear inequalities, the solution of each inequality is represented by a shaded area. The intersection of the two shaded areas represents the set of points that satisfy the conditions for the system.
(187) steps to graphing a quadratic function (Unit 6: Quadratic Functions - Lesson 3: Graphing Quadratic Functions)
1) put equation in standard form y=ax²+bx+c 2) determine direction of parabola [if a>0 it will open upwards and have a y-value minimum. If a<0 it will open downwards & will have a y-value maximum] 3) find the axis of symmetry (AoS) using the following formula: [x= -(b/2a)] 4) find the vertex [x-value for the vertex point is the AoS answer. Input the AoS x-value solution into original equation y=ax²+bx+c to find y-value for the vertex point. ] 5) y-intercept = c [The x-value of the y-intercept will always be 0 & the y-value is the same as c in the quadratic equation] 6) plot additional points by inputting x-values into equation & mirrored x-values to get the shape of the parabola
(198) steps to find the solution to a quadratic equation by factoring (Unit 6: Quadratic Functions - Lesson 7: Solving Quadratic Equations by Factoring)
1-Write the equation in standard quadratic form. 2-Factor. (Factor a GCF first, if possible, and then factor a trinomial if possible.) 3-Use the Zero Product Property. 4-Solve each equation. 5-Check your solutions. Example: x²+5x+4 -> you want to find two numbers that Add up to "b" which is 5 in this eg. & multiply together to get "c" = 4. Since 1 and 4 add up to 5 and multiply together to get 4, we can factor it like: (x+1)(x+4) // x=-1 or x=-4
(154) Power of a Product Property Pow-ofa-Prod-Prop (Unit 5: Exponents and Polynomials - Lesson 3: Multiplication & Division Properties of Exponents)
A product raised to a power is equal to the product of each factor raised to that power. If a ≠ 0 and m & n are integers, then (Pow-ofa-Prod-Prop):
(157) Negative Power of a Quotient Property -ve-Pow-ofa-Quo-Prop (Unit 5: Exponents and Polynomials - Lesson 3: Multiplication & Division Properties of Exponents)
A quotient raised to a negative power is equal to the reciprocal of the quotient raised to the opposite power. If a ≠ 0 and m & n are integers, then (-ve-Pow-ofa-Quo-Prop):
(200) rounded answer vs. radical form (Unit 6: Quadratic Functions - Lesson 8: Solving Quadratic Equations by Using Square Roots)
Solving a quadratic equation by finding its square roots works best if the constant is a perfect square, such as 4, 9, 16, 25, 36, 49, 64, etc. However, you can still find the solution even if the constant is not a perfect square. Your answer can be in a rounded answer or radical form. eg: x²=18 / x=√18 / x= +4.24 [rounded answer] - or - x²=18 / x= √2√9 / x= +3√2 [radical form]
(170) Degrees of Polynomials Table (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
The terms of a polynomial may be written in any order... - when possible, list terms in alphabetical order according to their variables (ie. 3x-4y+2z+2) - terms that contain the product of 2 or more variables (ie. 4xy+2xyz-3xz) it can be written in any order - if only 1 variable write it in standard form with the terms in order from the term with the highest degree to the term with the lowest degree [2x²+3x+4 instead of 3x+2x²+4 ]
(195) vertex form (Unit 6: Quadratic Functions - Lesson 5: Vertex Form of a Quadratic Equation)
The vertex form y=a (x-h)²+k of a quadratic equation can be used to find the vertex of a quadratic function. EXAMPLE of standard form to vertex form: y=ax²+bx+c ⟶⟶⟶ y=a (x-h)²+k y= -x²+6x+11 ⟶ (1) isolate a from x's as you work to making a perfect square trinomial equation y= -1(x²-6x)+11 ⟶ (2) find constant used in parenthesis of perfect sq. trinomial using formula =(b/2)² therefore (6/2)²=9 y+9= -1(x²-6x+9)+11 ⟶ (3) additions and subtractions on right side of equation also have to equal out on left side. Move left constant to right side of equation. y= -1(x²-6x+9)+11+((-9)ⓧ(-1)) ⟶ (4) when you move the +9 from left to right side of eq. it become -9 and then must be multiplied by the "a" constant that you originally pulled out from the parenthesis. That makes the +9 constants that were added on left & right of eq. equivalent. y= -(x²-6x+9)+20 ⟶ (5) simplify equation y= -(x-3)²+20
(140) When you multiply or divide each term of an inequality by a negative number, you must remember to reverse the symbol of inequality. (Unit 4: Systems of Equations & Inequalities - Lesson 7: Linear Inequalities in Two Variables)
When you multiply or divide each term of an inequality by a negative number, you must remember to reverse the symbol of inequality.
(171) difference of two squares (Unit 5: Exponents and Polynomials - Lesson 7: Special Products)
a binomial in the form [a²-b²] that results from the product of a binomial that is the sum of two terms and a binomial that is the difference of the same two terms
(125) transformation (Unit 3: Inequalities & Linear Functions - Lesson 10: Transformations in Linear Functions)
a change in the position, size, or shape of a figure, such as the graph of a function
(190) transformation of a function (Unit 6: Quadratic Functions - Lesson 4: Transformations of Quadratic Functions)
a change in the size, shape, or position of a function
(44) mixed number (Unit 1: Pre-Test Skills - Skill 14: Multiplication & Division of Fractions)
a combination of an integer and a fraction
(56) mathematical expression (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
a combination of terms with one or more operators grouped together to represent a numerical value
(93) compound inequality (Unit 3: Inequalities & Linear Functions - Lesson 3: Solving Multi-Step & Compound Inequalities)
a combination of two simple inequalities joined with the words "AND" or "OR"
(85) ratio (Unit 2: Expressions, Functions, & Equations - Lesson 8: Ratios, Proportions, Percentages, & Rates)
a comparison of two similar quantities using division
(95) disjunction (Unit 3: Inequalities & Linear Functions - Lesson 3: Solving Multi-Step & Compound Inequalities)
a compound inequality in which the two simple inequalities are separated by the word "OR"
(185) parabola (Unit 6: Quadratic Functions - Lesson 2: Characteristics of Quadratic Functions)
a curved line formed from a set of points that are all the same distance from a line, called a directrix, and a point, called a focus
(37) common factor (Unit 1: Pre-Test Skills - Skill 12: Greatest Common Factors)
a factor that is found in two or more given natural numbers
(43) improper fraction (Unit 1: Pre-Test Skills - Skill 14: Multiplication & Division of Fractions)
a fraction in which the numerator is equal to or larger than then the denominator
(46) proper fraction (Unit 1: Pre-Test Skills - Skill 14: Multiplication & Division of Fractions)
a fraction in which the numerator is smaller than the denominator
(105) linear function (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
a function in the form f(x) = mx + b that will graph as a straight line
(253) exponential function (Unit 8: Exponential & Radical Functions - Lesson 2: Exponential Functions)
a function in the form where and that will graph as a curved line Formula: y = abˣ , where a≠0, b≠1, & b>0 y - is the dependent variable x - is the independent variable
(177) quadratic function (Unit 6: Quadratic Functions - Lesson 1: Introduction to Quadratic Functions)
a function in the form ⨏(x)=ax²+bx+c, where a, b, and c are real numbers and a≠0 that will graph as a parabola
(98) continuous function (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
a function in which the coordinates for the data sets form a continuous, straight line
(275) square root function (Unit 8: Exponential & Radical Functions - Lesson 7: Radical Functions)
a function of the form ⨏(𝑥) = √𝑥 that contains a variable to the first power under the square root sign and that will graph as a curved line
(274) radical function (Unit 8: Exponential & Radical Functions - Lesson 7: Radical Functions)
a function that contains a radical expression
(100) discrete function (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
a function with a graph consisting of a finite number of points that do not connect
(107) scatterplot (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
a graph with points plotted on a coordinate plane to show a relationship between two data sets
(245) scatter plot (Unit 7: Data & Statistics - Lesson 6: Scatter Plots & Trends)
a graph with points plotted on a coordinate plane to show a relationship between two data sets
(129) system (Unit 4: Systems of Equations & Inequalities - Lesson 1: Systems of Linear Equations)
a group of similar and related elements considered together
(234) population (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
a large group of individuals selected for a statistical study
(181) directrix of a parabola (Unit 6: Quadratic Functions - Lesson 2: Characteristics of Quadratic Functions)
a line perpendicular to the axis of symmetry that lies outside a parabola that helps determine the shape of a parabola
(252) asymptote (Unit 8: Exponential & Radical Functions - Lesson 2: Exponential Functions)
a line that a graphed curve gets closer to but never touches as the value of a variable gets extremely small or extremely large
(166) polynomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
a mathematical expression consisting of a monomial or the sum or difference of two or more monomials
(164) monomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
a mathematical expression consisting of a single term containing a constant, a variable, or the product of a coefficient with one or more variables raised to whole-number powers
(168) trinomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
a mathematical expression consisting of the sum or difference of exactly three monomials
(158) binomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
a mathematical expression consisting of the sum or difference of exactly two monomials
(2) integer (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
a member of the set of numbers that includes positive numbers with no fractional parts, plus negative numbers with no fractional parts, plus zero
(132) substitution (Unit 4: Systems of Equations & Inequalities - Lesson 4: Substitution)
a method of solving systems of linear equations by substituting an expression for a variable and then solving for the other variable
(133) Gaussian elimination (Unit 4: Systems of Equations & Inequalities - Lesson 5: Elimination)
a method of solving systems of linear functions by adding equations together
(149) scientific notation (Unit 5: Exponents and Polynomials - Lesson 2: Power of Ten & Scientific Notation)
a method of writing very large or very small numbers in the form of a number that is equal to or greater than 1 and less than 10 multiplied by a power of ten
(9) whole number (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
a nonnegative number or zero with no fractional part
(4) natural number (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
a nonnegative number with no fractional part
(12) additive inverses (Unit 1: Pre-Test Skills - Skill 2: Addition & Subtraction of Real Numbers)
a number and its opposite whose sum is zero
(3) irrational number (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
a number that cannot be expressed as a ratio of two integers
(26) root (Unit 1: Pre-Test Skills - Skill 7: Powers, Exponents, & Roots)
a number that when multiplied by itself a certain number of times equals a given number: 3 (the root) is a square root of 9 (a given number) because so
(1) imaginary number (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
a number whose square is less than zero
(14) opposite (Unit 1: Pre-Test Skills - Skill 2: Addition & Subtraction of Real Numbers)
a number with the same absolute value as another number but with the opposite sign
(182) focus of a parabola (Unit 6: Quadratic Functions - Lesson 2: Characteristics of Quadratic Functions)term-181
a point inside the parabola that helps determine the shape of the curve
(163) linear polynomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
a polynomial with a degree of 1
(167) quadratic polynomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
a polynomial with a degree of 2 [examples: 4xy, or 3x²-4y, or 2x²+4x+4]
(159) cubic polynomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
a polynomial with a degree of 3 [examples: 4xyz, or 2x²y, or 3x³-4y²+2z+2]
(236) sample (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
a portion of a population selected to represent the population
(267) root (Unit 8: Exponential & Radical Functions - Lesson 4: Radical Expressions)
a quantity or value, which, when multiplied by itself a certain number of times, equals a given quantity or value eg. ⁴√625𝑥⁸𝑦¹²𝓏⁴ = 5𝑥²𝑦³𝓏
(86) unit rate (Unit 2: Expressions, Functions, & Equations - Lesson 8: Ratios, Proportions, Percentages, & Rates)
a rate in which the second quantity is written as 1 unit
(80) conversion factor (Unit 2: Expressions, Functions, & Equations - Lesson 8: Ratios, Proportions, Percentages, & Rates)
a ratio that is used to convert one unit of measurement to a different unit of measurement
(70) function (Unit 2: Expressions, Functions, & Equations - Lesson 4: Relations: Functions, Equations & Inequalities)
a relation in which every input is paired with exactly one output
(69) equation (Unit 2: Expressions, Functions, & Equations - Lesson 4: Relations: Functions, Equations & Inequalities)
a relation in which one expression is equal to another expression
(72) inequality (Unit 2: Expressions, Functions, & Equations - Lesson 4: Relations: Functions, Equations & Inequalities)
a relation in which one expression is not equal to another expression
(87) inequality (Unit 3: Inequalities & Linear Functions - Lesson 1: Understanding)
a relation in which one expression is not equal to another expression
(139) linear inequality (Unit 4: Systems of Equations & Inequalities - Lesson 7: Linear Inequalities in Two Variables)
a relation in which the expression on one side of the relation symbol does not equal the expression on the other side, and the statement can be written with any of the four symbols of inequality in the form Ax + By > C
(51) relation (Unit 2: Expressions, Functions, & Equations - Lesson 1: What is Algebra?)
a relationship between sets of information
(242) negative correlation (Unit 7: Data & Statistics - Lesson 6: Scatter Plots & Trends)
a relationship between two quantities in which an increase in one is accompanied by a decrease in the other
(244) positive correlation (Unit 7: Data & Statistics - Lesson 6: Scatter Plots & Trends)
a relationship between two quantities in which an increase in one is accompanied by an increase in the other
(243) no correlation (Unit 7: Data & Statistics - Lesson 6: Scatter Plots & Trends)
a relationship between two quantities in which both quantities may increase or decrease independently of what happens with the other quantity
(113) direct variation (Unit 3: Inequalities & Linear Functions - Lesson 7: Direct & Inverse Variation)
a relationship between two variables whose ratio remains a nonzero constant, because if one variable increases the other variable increases in proportion
(114) inverse variation (Unit 3: Inequalities & Linear Functions - Lesson 7: Direct & Inverse Variation)
a relationship in which the product of the value of the variables remain a nonzero constant because if one variable increases the other variable decreases in proportion
(213) function (Unit 7: Data & Statistics - Lesson 1: Analyzing & Organizing Data)
a relationship that pairs each input with exactly one output and can be represented by ordered pairs or a mapping diagram
(271) extraneous root (Unit 8: Exponential & Radical Functions - Lesson 6: Solving Radical Equations)
a root that is introduced into an equation in the process of solving the equation but does not satisfy the conditions of the original equation
(235) random sample (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
a sample that is chosen without any particular preference and which represents an entire population
(248) geometric sequence (Unit 8: Exponential & Radical Functions - Lesson 1: Geometric Sequences & Series)
a sequence in which the ratio between consecutive terms is constant
(108) arithmetic sequence (Unit 3: Inequalities & Linear Functions - Lesson 5: Arithmetic Sequences)
a sequence of numbers in which the difference between each term is the same nonzero number
(123) family of functions (Unit 3: Inequalities & Linear Functions - Lesson 10: Transformations in Linear Functions)
a set of functions such that the graph of each member of the family has certain common characteristics
(111) sequence (Unit 3: Inequalities & Linear Functions - Lesson 5: Arithmetic Sequences)
a set of numbers with a specific pattern
(66) order of operations (Unit 2: Expressions, Functions, & Equations - Lesson 3: Simplifying Expressions)
a set of rules used to determine the proper order for performing operations in an expression that involves more than one operation
(232) census (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
a statistical study of an entire population
(143) exponent (Unit 5: Exponents and Polynomials - Lesson 1: Integer Exponents)
a symbol or number that indicates the power to which a base is raised
(58) operator (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
a symbol that indicates a mathematical operation, such as addition, subtraction, multiplication, or division (+, −, ×, ÷)
(59) relation symbol (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
a symbol that shows the relationship between two expressions, that they are either equal, indicated with an equal sign (=), or unequal, indicated with an inequality sign (< or >)
(135) consistent system (Unit 4: Systems of Equations & Inequalities - Lesson 6: Special Systems)
a system of linear equations that has at least one solution
(138) independent system (Unit 4: Systems of Equations & Inequalities - Lesson 6: Special Systems)
a system of linear equations that has exactly one solution
(137) inconsistent system (Unit 4: Systems of Equations & Inequalities - Lesson 6: Special Systems)
a system of linear equations that has no solution
(136) dependent system (Unit 4: Systems of Equations & Inequalities - Lesson 6: Special Systems)
a system of linear equations with an infinite number of solutions
(214) frequency table (Unit 7: Data & Statistics - Lesson 2: Frequency Tables, Histograms, & Stem-and-Leaf Plots)
a table showing the frequency of each data value
(212) trend (Unit 7: Data & Statistics - Lesson 1: Analyzing & Organizing Data)
a tendency in a certain direction
(188) dilation of a quadratic function (Unit 6: Quadratic Functions - Lesson 4: Transformations of Quadratic Functions)
a transformation of a quadratic function that is represented by a parabola that becomes wider or narrower than the original parabola
(191) translation of a quadratic function (Unit 6: Quadratic Functions - Lesson 4: Transformations of Quadratic Functions)
a transformation of a quadratic function that is represented by a parabola that is shifted up, down, left, or right of the original parabola
(189) reflection of a quadratic function (Unit 6: Quadratic Functions - Lesson 4: Transformations of Quadratic Functions)
a transformation of a quadratic function that is represented by a parabola that opens the opposite direction of the original parabola
(126) translation (Unit 3: Inequalities & Linear Functions - Lesson 10: Transformations in Linear Functions)
a transformation that moves each point the same distance in the same direction
(172) perfect square trinomial (Unit 5: Exponents and Polynomials - Lesson 7: Special Products)
a trinomial in the form "a² + 2ab + b² or a² - 2ab + b²" that results from the product of the square of a binomial
(174) quadratic trinomial (Unit 5: Exponents and Polynomials - Lesson 9: Factoring Quadratic Trinomials)
a trinomial in the form x² + bx + c or ax²x + c with a degree of 2
(27) coordinate plane (Unit 1: Pre-Test Skills - Skill 8: Coordinate Planes)
a two-dimensional surface on which points are plotted and located by their x and y coordinates
(220) measure of central tendency (Unit 7: Data & Statistics - Lesson 3: Measure of Central Tendency)
a value or values around which the values in a statistical data set tend to cluster or group; the mean, median, and mode of a statistical data set
(228) percentile (Unit 7: Data & Statistics - Lesson 4: Measure of Variation)
a value that divides a statistical data set into 100 groups having an equal number of values
(209) frequency of data (Unit 7: Data & Statistics - Lesson 1: Analyzing and Organizing Data)
a value that expresses how often a piece of data appears in a data set
(223) outlier (Unit 7: Data & Statistics - Lesson 3: Measure of Central Tendency)
a value that is well outside the range of all the other values in a statistical data set
(62) variable (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
a value, usually in the form of a letter or symbol, that can change or that represents an unknown quantity
(63) first-degree variable (Unit 2: Expressions, Functions, & Equations - Lesson 3: Simplifying Expressions)
a variable raised to the power of 1
(67) second-degree variable (Unit 2: Expressions, Functions, & Equations - Lesson 3: Simplifying Expressions)
a variable raised to the power of 2
(180) axis of symmetry of a parabola (Unit 6: Quadratic Functions - Lesson 2: Characteristics of Quadratic Functions)
a vertical line that divides a parabola into two halves that are identical in size and shape, but reversed in direction (formula: x=-(b/2a) )
(215) histogram (Unit 7: Data & Statistics - Lesson 2: Frequency Tables, Histograms, & Stem-and-Leaf Plots)
a visual representation of data frequency using adjacent vertical bars whose heights are based on the frequency of the data
(206) circle graph (Unit 7: Data & Statistics - Lesson 1: Analyzing & Organizing Data)
a visual representation of data in which a circle is divided into sectors, each of which represents a percent of the whole data set
(205) bar graph (Unit 7: Data & Statistics - Lesson 1: Analyzing & Organizing Data)
a visual representation of data using horizontal or vertical bars whose lengths are related to the frequency of the data
(210) line graph (Unit 7: Data & Statistics - Lesson 1: Analyzing & Organizing Data)
a visual representation of data using line segments
(216) stem-and-leaf plot (Unit 7: Data & Statistics - Lesson 2: Frequency Tables, Histograms, & Stem-and-Leaf Plots)
a visual representation of numerical data in which each number in a set of numbers is split into a stem, formed by the greatest common place value of the set, and a leaf, formed by the next greatest common place value of the set
(225) box-and-whisker plot (Unit 7: Data & Statistics - Lesson 4: Measure of Variation)
a visual representation of numerical data that shows how values within a data set are distributed
(217) domain of a parabola (Unit 7: Data & Statistics - Lesson 2: Frequency Tables, Histograms, & Stem-and-Leaf Plots)
all x values included in a function
(218) range of a parabola (Unit 7: Data & Statistics - Lesson 2: Frequency Tables, Histograms, & Stem-and-Leaf Plots)
all y values included in a function
(247) function formula (Unit 8: Exponential & Radical Functions - Lesson 1: Geometric Sequences & Series)
allows directly finding any term in a geometric sequence
(250) recursive formula (Unit 8: Exponential & Radical Functions - Lesson 1: Geometric Sequences & Series)
allows finding the next term in a geometric sequence using the preceding term or terms
(151) exponential expression (Unit 5: Exponents and Polynomials - Lesson 3: Multiplication & Division Properties of Exponents)
an algebraic expression that contains at least one term containing an exponent
(259) interest (Unit 8: Exponential & Radical Functions - Lesson 3: Exponential Growth & Decay)
an amount of money that is charged for the use of credit or for borrowing money, or an amount of money paid to a person for an investment
(273) radical equation (Unit 8: Exponential & Radical Functions - Lesson 6: Solving Radical Equations)
an equation that contains a variable within a radical expression
(79) formula (Unit 2: Expressions, Functions, & Equations - Lesson 7: Using Formulas)
an equation that expresses a mathematical rule or relationship
(83) proportion (Unit 2: Expressions, Functions, & Equations - Lesson 8: Ratios, Proportions, Percentages, & Rates)
an equation that states that two ratios are equal
(128) linear equation (Unit 4: Systems of Equations & Inequalities - Lesson 1: Systems of Linear Equations)
an equation whose graph is a straight line
(25) power (Unit 1: Pre-Test Skills - Skill 7: Powers, Exponents, & Roots)
an exponent
(144) integer exponent (Unit 5: Exponents and Polynomials - Lesson 1: Integer Exponents)
an exponent consisting of an integer
(24) exponent (Unit 1: Pre-Test Skills - Skill 7: Powers, Exponents, & Roots)
an exponent tells how many times to multiply a number or term by itself
(264) radical expression (Unit 8: Exponential & Radical Functions - Lesson 4: Radical Expressions)
an expression that contains a radical symbol ( When simplifying, make sure the expression has none of the following: • root factors other than 1 in the radicand • fractions in the radicand • roots in the denominator of the expression ) eg.1) √(𝑎𝑏) = √𝑎 x √𝑏 eg.2) √(4/64) = (√4)/(√64) = 2/8 = 1/4 eg.3) √(𝑑/4) = (√𝑑)/(√4) = (√𝑑)/2 eg.4) ³√(64𝑎³𝑏⁹) = ³√(64) x ³√(𝑎) x ³√(𝑏) = 4 x 𝑎³÷³ x 𝑏⁹÷³ = 4𝑎𝑏³
(57) numerical expression (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
an expression that contains only numbers with one or more operators
(52) algebraic expression (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
an expression that contains variables or a combination of constants and variables with one or more operators
(103) function rule (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
an expression that defines a function
(6) positive integer (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
an integer with a value greater than zero
(5) negative integer (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
an integer with a value less than zero, a counting number
(130) solution of a linear system (Unit 4: Systems of Equations & Inequalities - Lesson 2: Graphing)
an ordered pair that satisfies all the equations in the system
(251) sequence (Unit 8: Exponential & Radical Functions - Lesson 1: Geometric Sequences & Series)
an ordered set of numbers
(81) indirect measurement (Unit 2: Expressioterm-72ns, Functions, & Equations - Lesson 8: Ratios, Proportions, Percentages, & Rates)
any method that uses formulas, figures, or proportions to measure an object
(7) rational number (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
any number that can be expressed as a ratio of two numbers, in which "a" & "b" are integers and "b" does not equal zero.
(175) perfect square (Unit 5: Exponents and Polynomials - Lesson 10: Factoring Special Products)
any number whose positive square root is a whole number
(8) real number (Unit 1: Pre-Test Skills - Skill 1: Real Numbers)
any rational or irrational number
(11) addend (Unit 1: Pre-Test Skills - Skill 2: Addition & Subtraction of Real Numbers)
any value added to another to form a sum
(17) factor (Unit 1: Pre-Test Skills - Skill 3: Multiplication of Real Numbers)
any value that is multiplied by another value to yield a product
(22) factor (Unit 1: Pre-Test Skills - Skill 6: Prime & Composite Numbers & Prime Factorization)
any value that is multiplied by another value to yield a product
(90) solution of an inequality (Unit 3: Inequalities & Linear Functions - Lesson 1: Understanding)
any value that satisfies the conditions on the inequality
(94) conjunction (Unit 3: Inequalities & Linear Functions - Lesson 3: Solving Multi-Step & Compound Inequalities)
compound inequality in which the two simple inequalities are separated by the word "AND"
(169) Polynomials Table (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
examples of the different polynomials
(148) power of ten (Unit 5: Exponents and Polynomials - Lesson 2: Power of Ten & Scientific Notation)
exponential expression with 10 as the base;
(207) data (Unit 7: Data & Statistics - Lesson 1: Analyzing & Organizing Data)
facts, statistics, and pieces of information
(231) bias (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
favoring one or more parts of a population over the others
(20) estimate (Unit 1: Pre-Test Skills - Skill 5: Estimation With Rounding)
find the approximate answer
(55) evaluate an expression (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
find the numerical value of an expression by substituting a number for each variable and simplifying the expression
(192) zero of a function (Unit 6: Quadratic Functions - Lesson 4: Transformations of Quadratic Functions)
for any function, a value for x that causes y to equal 0; the x-value at the coordinate where the graph of a function crosses the x-axis
(30) equivalent fractions (Unit 1: Pre-Test Skills - Skill 9: Equivalent Fractions)
fractions that are equal in value
(208) data sets (Unit 7: Data & Statistics - Lesson 1: Analyzing & Organizing Data)
groups of data that have similar qualities or characteristics
(255) compound interest (Unit 8: Exponential & Radical Functions - Lesson 3: Exponential Growth & Decay)
interest earned or paid based on both the principal and previously paid interest
(262) simple interest (Unit 8: Exponential & Radical Functions - Lesson 3: Exponential Growth & Decay)
interest earned or paid on the principal
(120) parallel lines (Unit 3: Inequalities & Linear Functions - Lesson 9: Slope-Intercept Formula & Point-Slope Formula)
lines in the same plane that have no points in common
(121) perpendicular lines (Unit 3: Inequalities & Linear Functions - Lesson 9: Slope-Intercept Formula & Point-Slope Formula)
lines that intersect to form right angles (90°)
(211) statistics (Unit 7: Data & Statistics - Lesson 1: Analyzing & Organizing Data)
numerical data
(229) quartile (Unit 7: Data & Statistics - Lesson 4: Measure of Variation)
one of three values that divide a statistical data set into four groups having an equal number of values
(89) inverse operations (Unit 3: Inequalities & Linear Functions - Lesson 1: Understanding)
operations that are opposite and cancel each other out; addition and subtraction are inverse operations; multiplication and division are inverse operations
(92) inverse operations
operations that are opposite and cancel each other out; addition and subtraction are inverse operations; multiplication and division are inverse operations
(88) inverse (Unit 3: Inequalities & Linear Functions - Lesson 1: Understanding)
opposite in position, direction, order, or effect
(91) inverse (Unit 3: Inequalities & Linear Functions - Lesson 2: Solving Inequalities)
opposite in position, direction, order, or effect
(61) term (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
part of a mathematical expression consisting of a constant, or a variable, or the product of a number and a variable, separated from other terms by an operator or a relation symbol
(60) simplify an expression (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
perform all the indicated operations
(179) a≠0 but b and/or c = 0 (Unit 6: Quadratic Functions - Lesson 1: Introduction to Quadratic Functions)
quadratic function special note:
(269) like radicals (Unit 8: Exponential & Radical Functions - Lesson 5: Working with Radical Expressions)
radical expressions that have the same terms in their radicands
(36) simplified (Unit 1: Pre-Test Skills - Skill 11: Writing Fractions in Simplest Terms)
reduced to lowest terms
(49) conceptual (Unit 2: Expressions, Functions, & Equations - Lesson 1: What is Algebra?)
relating to abstract ideas
(239) systematic random sampling (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
sampling in which members of the sample are chosen according to a specified time or time interval
(238) stratified random sampling (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
sampling in which the population is first divided into similar, non-overlapping groups, or strata, from which random samples are chosen
(237) simple random sampling (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
sampling that creates a random sample by choosing members that are just as likely to be picked as any other member
(270) rationalize a denominator (Unit 8: Exponential & Radical Functions - Lesson 5: Working with Radical Expressions)
simplify an expression so that there are no radical expressions in the denominator
(32) least common multiple (LCM) (Unit 1: Pre-Test Skills - Skill 10: Least Common Multiples & Least Common Denominators)
smallest multiple that is common to two or more numbers
(64) grouping symbols (Unit 2: Expressions, Functions, & Equations - Lesson 3: Simplifying Expressions)
symbols that are used to indicate a group of terms that should be treated as one term or to indicate operations that must be performed before other operations are attempted in an expression; (), [ ], { }
(146) Table 1 (Unit 5: Exponents and Polynomials - Lesson 1: Integer Exponents)
table showing examples of different types of exponents
(150) table 1 (Unit 5: Exponents and Polynomials - Lesson 2: Power of Ten & Scientific Notation)
table showing examples of different types scientific notation
(147) Table 2 (Unit 5: Exponents and Polynomials - Lesson 1: Integer Exponents)
table showing rules for integer exponents
(65) like terms (Unit 2: Expressions, Functions, & Equations - Lesson 3: Simplifying Expressions)
terms that contain the same set of variables raised to the same power
(258) half-life (Unit 8: Exponential & Radical Functions - Lesson 3: Exponential Growth & Decay)
the amount of time required for one-half of the mass of a radioactive substance to decay into another substance
(19) quotient (Unit 1: Pre-Test Skills - Skill 4: Division of Real Numbers)
the answer in a division problem
(18) product (Unit 1: Pre-Test Skills - Skill 3: Multiplication of Real Numbers)
the answer in a multiplication problem
(40) difference (Unit 1: Pre-Test Skills - Skill 13: Addition & Subtraction of Fractions)
the answer in a subtraction problem
(42) sum (Unit 1: Pre-Test Skills - Skill 13: Addition & Subtraction of Fractions)
the answer in an addition problem
(47) quotient (Unit 1: Pre-Test Skills - Skill 14: Multiplication & Division of Fractions)
the answer to a division problem
(45) product (Unit 1: Pre-Test Skills - Skill 14: Multiplication & Division of Fractions)
the answer to a multiplication problem
(35) denominator (Unit 1: Pre-Test Skills - Skill 11: Writing Fractions in Simplest Terms)
the bottom number in a fraction that shows the number of equal parts in the whole
(39) denominator (Unit 1: Pre-Test Skills - Skill 13: Addition & Subtraction of Fractions)
the bottom number in a fraction that shows the number of equal parts in the whole
(48) algebra (Unit 2: Expressions, Functions, & Equations - Lesson 1: What is Algebra?)
the branch of mathematics that uses alphabetic symbols to represent unknown numbers or specific sets of numbers in order to make generalizations about arithmetic operations and mathematical relationships
(162) leading coefficient (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
the coefficient of the first term of a polynomial when the polynomial is written in standard form
(257) exponential decay (Unit 8: Exponential & Radical Functions - Lesson 3: Exponential Growth & Decay)
the decrease in number or size of a system at an increasingly rapid rate in proportion to its decreasing number or size
(161) degree of a polynomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
the degree of the monomial with the greatest degree within a polynomial (using the example in the picture the degree of the Polynomial is 9 since 9 is the highest exponent of the three groupings)
(109) common difference (Unit 3: Inequalities & Linear Functions - Lesson 5: Arithmetic Sequences)
the difference between each term in an arithmetic sequence
(230) range (Unit 7: Data & Statistics - Lesson 4: Measure of Variation)
the difference between the greatest and the least values in a statistical data set
(226) interquartile range (Unit 7: Data & Statistics - Lesson 4: Measure of Variation)
the difference between the upper and lower quartile of a statistical data set (IQR = Q₃-Q₁)
(178) second difference (Unit 6: Quadratic Functions - Lesson 1: Introduction to Quadratic Functions)
the difference in values between the values of the first differences
(116) run (Unit 3: Inequalities & Linear Functions - Lesson 8: Intercepts & Slope)
the difference in x-values between the coordinates of two points on a line
(115) rise (Unit 3: Inequalities & Linear Functions - Lesson 8: Intercepts & Slope)
the difference in y-values between the coordinates of two points on a line
(176) first differences (Unit 6: Quadratic Functions - Lesson 1: Introduction to Quadratic Functions)
the differences in y-values produced by a constant change in x-values in a function
(10) absolute value (Unit 1: Pre-Test Skills - Skill 2: Addition & Subtraction of Real Numbers)
the distance from zero to a number on the number line
(256) depreciation (Unit 8: Exponential & Radical Functions - Lesson 3: Exponential Growth & Decay)
the exponential decrease of the value of a purchased object
(266) radicand (Unit 8: Exponential & Radical Functions - Lesson 4: Radical Expressions)
the expression under a radical symbol eg. ⁴√ 625𝑥⁸𝑦¹²𝓏⁴ = 5𝑥²𝑦³𝓏
(102) function notation (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
the form of a function written as f(x) when x is the independent variable
(261) radioactive decay (Unit 8: Exponential & Radical Functions - Lesson 3: Exponential Growth & Decay)
the gradual changing of a radioactive substance into another substance
(186) vertex of a parabola (Unit 6: Quadratic Functions - Lesson 2: Characteristics of Quadratic Functions)
the highest or lowest point on the graph of a quadratic function [ x-value for the vertex point is the Axis of Symmetry answer {x=-(b/2a)}. Input that x-value solution into original equation y=ax²+bx+c to find y-value for the vertex point. (x,y)]
(254) exponential growth (Unit 8: Exponential & Radical Functions - Lesson 2: Exponential Functions)
the increase in number or size of a system at an increasingly rapid rate in proportion to its growing number or size
(71) independent variable (Unit 2: Expressions, Functions, & Equations - Lesson 4: Relations: Functions, Equations & Inequalities)
the input of a function
(104) independent variable (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
the input variable of a function
(241) independent variable (Unit 7: Data & Statistics - Lesson 6: Scatter Plots & Trends)
the input variable of a function whose value determines the value of the dependent variable
(31) least common denominator (LCD) (Unit 1: Pre-Test Skills - Skill 10: Least Common Multiples & Least Common Denominators)
the least common multiple of two or more denominators
(221) median (Unit 7: Data & Statistics - Lesson 3: Measure of Central Tendency)
the middle number in a statistical data set that is arranged in numerical order
(15) subtrahend (Unit 1: Pre-Test Skills - Skill 2: Addition & Subtraction of Real Numbers)
the number being subtracted in a subtraction problem
(13) minuend (Unit 1: Pre-Test Skills - Skill 2: Addition & Subtraction of Real Numbers)
the number from which another number is subtracted in a subtraction problem
(145) power (Unit 5: Exponents and Polynomials - Lesson 1: Integer Exponents)
the number of times a base is used as a factor indicated by an exponent
(53) coefficient (Unit 2: Expressions, Functions, & Equations - Lesson 2: The Language of Algebra)
the number written together with a variable to indicate the product of the number and the variable in a term
(260) principal (Unit 8: Exponential & Radical Functions - Lesson 3: Exponential Growth & Decay)
the original amount of money that is borrowed or invested
(68) dependent variable (Unit 2: Expressions, Functions, & Equations - Lesson 4: Relations: Functions, Equations & Inequalities)
the output of a function
(240) dependent variable (Unit 7: Data & Statistics - Lesson 6: Scatter Plots & Trends)
the output variable in a function that changes based on the changes of the independent variable
(99) dependent variable (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
the output variable of a function
(203) discriminant (Unit 6: Quadratic Functions - Lesson 10: Solving Quadratic Equations with the Quadratic Formula)
the part of the quadratic formula that determines the number of roots which are also x-intercepts. It is the part of quadratic formula under the radical sign, or b²-4ac if the value of the discriminant is: +ve = 2 roots (eg. 3x²-5x+1=0 // b²-4ac= 13 ) 0 = 1 root (eg. 2x²-12x+18=0 // (12)²-4(2)(18)= 0 ) -ve = no roots (eg. 5x²-3x+4=0 // (3)²-4(5)(4)= -71 )
(29) origin (Unit 1: Pre-Test Skills - Skill 8: Coordinate Planes)
the point (0, 0) where the horizontal axis intersect the vertical axis on a coordinate plane
(127) intersection (Unit 4: Systems of Equations & Inequalities - Lesson 1: Systems of Linear Equations)
the point that two lines have in common; their point of crossing
(272) principal root (Unit 8: Exponential & Radical Functions - Lesson 6: Solving Radical Equations)
the positive real root of a positive number
(38) greatest common factor (GCF) (Unit 1: Pre-Test Skills - Skill 12: Greatest Common Factors)
the product of the common prime factors of two or more natural numbers
(246) common ratio (Unit 8: Exponential & Radical Functions - Lesson 1: Geometric Sequences & Series)
the ratio of a term with the previous term in a geometric sequence
(84) rate (Unit 2: Expressions, Functions, & Equations - Lesson 8: Ratios, Proportions, Percentages, & Rates)
the ratio of the amount of change of one quantity relative to another quantity
(117) slope (Unit 3: Inequalities & Linear Functions - Lesson 8: Intercepts & Slope)
the ratio of the rise over the run of a line
(16) sum (Unit 1: Pre-Test Skills - Skill 2: Addition & Subtraction of Real Numbers)
the result of an addition problem
(33) multiple (Unit 1: Pre-Test Skills - Skill 10: Least Common Multiples & Least Common Denominators)
the result of multiplying a number by an integer
(233) data sampling (Unit 7: Data & Statistics - Lesson 5: Sampling & Bias)
the selection of a sample to estimate the characteristics of an entire population
(110) ellipsis (Unit 3: Inequalities & Linear Functions - Lesson 5: Arithmetic Sequences)
the series of three dots at the end of a number sequence that indicates that the sequence continues in the same manner
(96) intersection of two sets (Unit 3: Inequalities & Linear Functions - Lesson 3: Solving Multi-Step & Compound Inequalities)
the set of elements that could be found in both sets at the same time
(97) union of two sets (Unit 3: Inequalities & Linear Functions - Lesson 3: Solving Multi-Step & Compound Inequalities)
the set of elements that could be found in one set or the other
(101) domain (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
the set of input data in a relation
(106) range (Unit 3: Inequalities & Linear Functions - Lesson 4: Understanding Functions)
the set of output data in a relation
(76) solution set (Unit 2: Expressions, Functions, & Equations - Lesson 5: Solving Equations With Addition & Subtraction)
the set of values that makes the equation true
(50) derivation (Unit 2: Expressions, Functions, & Equations - Lesson 1: What is Algebra?)
the source or origin of a word
(219) mean (Unit 7: Data & Statistics - Lesson 3: Measure of Central Tendency)
the sum of all the values in a data set divided by the number of values in the set
(160) degree of a monomial (Unit 5: Exponents and Polynomials - Lesson 4: Introduction to Polynomials)
the sum of the exponents of the variables of a monomial
(249) geometric series (Unit 8: Exponential & Radical Functions - Lesson 1: Geometric Sequences & Series)
the sum of the terms of a geometric sequence
(265) radical symbol (Unit 8: Exponential & Radical Functions - Lesson 4: Radical Expressions)
the symbol that indicates the root of an expression = √
(82) means and extremes (Unit 2: Expressions, Functions, & Equations - Lesson 8: Ratios, Proportions, Percentages, & Rates)
the terms that are opposite each other both across the equals sign and across the division symbol in a proportion
(41) numerator (Unit 1: Pre-Test Skills - Skill 13: Addition & Subtraction of Fractions)
the top number in a fraction that shows the number of equal parts being considered
(142) base (Unit 5: Exponents and Polynomials - Lesson 1: Integer Exponents)
the value being raised to a power
(222) mode (Unit 7: Data & Statistics - Lesson 3: Measure of Central Tendency)
the value or values that occur most often in a statistical data set
(227) measure of variation (Unit 7: Data & Statistics - Lesson 4: Measure of Variation)
the value that describes the spread of the values in a statistical data set; the range of a statistical data set
(112) constant of variation (Unit 3: Inequalities & Linear Functions - Lesson 7: Direct & Inverse Variation)
the value that relates two variables that are directly proportional or inversely proportional to each other
(73) input (Unit 2: Expressions, Functions, & Equations - Lesson 4: Relations: Functions, Equations & Inequalities)
the variable that determines the value of the output in a function
(74) output (Unit 2: Expressions, Functions, & Equations - Lesson 5: Solving Equations With Addition & Subtraction)
the variable whose value depends on the input in a function
(118) x-intercept (Unit 3: Inequalities & Linear Functions - Lesson 8: Intercepts & Slope)
the x-coordinate of the point at which a line intersects the x-axis of a coordinate plane
(119) y-intercept (Unit 3: Inequalities & Linear Functions - Lesson 8: Intercepts & Slope)
the y-coordinate of the point at which a line intersects the y-axis of a coordinate plane
(183) maximum of a quadratic function (Unit 6: Quadratic Functions - Lesson 2: Characteristics of Quadratic Functions)
the y-value of the coordinate of the vertex of a parabola that opens downward
(184) minimum of a quadratic function (Unit 6: Quadratic Functions - Lesson 2: Characteristics of Quadratic Functions)
the y-value of the coordinate of the vertex of a parabola that opens upward
(202) the quadratic formula (Unit 6: Quadratic Functions - Lesson 10: Solving Quadratic Equations with the Quadratic Formula)
to find exact solutions with any type of quadratic equation is this formula: x= [-b±√(b²-4ac)] / 2a (different types of problems lend themselves toward certain methods of solution solve quadratic equations by graphing-lesson 6, factoring-lesson 7, finding the square roots lesson-8, or by completing the square lesson-9 can all be replaced by this new found formula in lesson-10).
(122) dilation (of a line) (Unit 3: Inequalities & Linear Functions - Lesson 10: Transformations in Linear Functions)
transformation that causes a stretching away from an axis or compressing toward an axis
(28) ordered pair (Unit 1: Pre-Test Skills - Skill 8: Coordinate Planes)
two numbers used to identify a point on a coordinate plane
(78) reciprocals (Unit 2: Expressions, Functions, & Equations - Lesson 6: Solving Equations With Multiplication & Division)
two numbers whose product is 1; reciprocals are also called multiplicative inverses
(21) composite numbers (Unit 1: Pre-Test Skills - Skill 6: Prime & Composite Numbers & Prime Factorization)
whole numbers with more than two factors
(196) roots of a quadratic function (Unit 6: Quadratic Functions - Lesson 6: Solving Quadratic Equations by Graphing)
⟶ the solutions to a quadratic function; the zeros of a quadratic function. ================== ⟶ A quadratic function may have one root, two roots, or no real roots. (y=0) ⟶ Graphing is a good way to visualize the roots of a quadratic function. However, it is the least reliable method of finding the roots. The reason for that is that so many quadratic functions have roots that are not whole numbers. If a root is a fraction, it will lie between two grids on the graph, which makes it hard to arrive at the exact value. So, it is usually best to use another method to find the roots of a quadratic equation.
summary of transformations of functions
⨏(x)= x²+c ⟶ translation up (c>0) ⨏(x)= x²-c ⟶ translation down (c>0) ⨏(x+c)= (x+c)² ⟶ translation left (c>0) ⨏(x-c)= (x-c)² ⟶ translation right (c>0) ⨏(x)= ax² ⟶ narrower dilation if |a| > 1 ⨏(x)= ax² ⟶ wider dilation if |a| < 1 ⨏(x)= x² ⟶ opens upward ⨏(x)= -x² ⟶ opens downward (reflection)
