algebra 1
Zero Product Property
when the product of two or more factors is zero, one of these factors must equal zero
x-intercept
where the graph crosses the x-axis
y-intercept
where the line crosses the y axis
maximum
(n.) the greatest possible amount or degree; (adj.) reaching the greatest possible amount or degree
minimum
(n.) the smallest possible amount; (adj.) the lowest permissible or possible
perfect cubes
1, 8, 27, 64, 125, 216,343
perfect square
1,4,9,16,25,36,49,64,81,100,121,144,169,196,225
arithmetic sequence
A sequence where each term is the sum of the previous term and a common difference, 𝑑
Closure Property
A set of numbers is said to be closed for a specific mathematical operation when the result obtained after performing the operation on two elements of the set always produces an element of the same set
equation
A statement that the values of two mathematical expressions are equal (indicated by the sign =)
Stretching a function
Multiplying a function by a coefficient greater than
Communative Property
Number order can be changed without changing the answer
irrational numbers
Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.
leading coefficient
The coefficient of the term with the highest degree
OR Inequality
The compound inequality is true if at least one of the statements is true
and inequality
The compound inequality is true only if both statements are true
GCF
The greatest factor that divides two numbers
degree of a polynomial
The highest degree of any monomial or term in the polynomial
vertex
The maximum or minimum point of a parabola
relative minimum
The point on a graph where the interval changes from decreasing to increasing
relative maximum
The point on a graph where the interval changes from increasing to decreasing
negative slope
The value of the slope in the function is negative; also, when a functions is decreasing.
residual
The vertical distance between an actual data point and the predicted value of the function fitted to the data
stander form of a polynomial
When the monomial terms of a polynomial expression are organized in descending degree order from left to right
function notation
Writing algebraic variables as functions of other variables, like 𝑓(𝑥) = 4𝑥 (which is read "the function of 𝑥 equals 4𝑥," so basically f takes 𝑥 and multiplies it by 4).
vertex form
Given 𝑎(𝑥−h)2+𝑘,(h,𝑘)is the vertex of a parabola
Histogram
A bar-style data display showing the frequency of data measured over intervals, rather than displaying each individual data value
box plot
A box and whisker diagram that display the five-number summary for a data set (minimum, first quartile, median, third quartile, and maximum values)
term
A constant, variable, or multiplicative combination of the two
Parabola
A curved symmetrical U-shaped graph that is the graphic representation of a quadratic function; it may open up or down
constant
A fixed value within an equation or expression (a number or letter that stands for a fixed number)
recursive formula
A formula to solve for a term using the computation of all previous terms
explict formula
A formula to solve for a term using the first term of the sequence and the fixed rule for the sequence
Dot Plot
A graphical representation where each data value is represented with a dot above a number line
Variable
A letter that represents a quantity that may change within the context of a problem
slope
A measure of the steepness of a line or a section of a line calculated by connecting two points and dividing the change in the dependent values by the change in the independent values
factor
A number or quantity that when multiplied by another produces a given number or expression
Coefficient
A number used to multiply a variable
ordered pairs
A pair of numbers used to locate a point or a location on a coordinate plane; the first number (usually x) tells how far to move horizontally and the second number (usually y) tells how far to move vertically
rate of change
A rate that describes how one quantity changes in relation to another quantity
rational numbers
A real number including those with a fractional or decimal part; it can be written in the form a/b, where a and b are integers
function
A relationship between input and output, where each input has a single output
geometric sequence
A sequence of numbers in which each term is the product of the previous term and some real number
coordinate plane
A two-dimensional surface on which points, lines and curves can be plotted ; it has two scales, called the x-axis (a horizontal number line) and y- axis (a vertical number line) and four quadrants with positive and negative numbers in both axes.
input
A value assigned to the known variable in a function
dependent variable
A variable whose variation depends on that of another (output, range)
independent variable
A variable whose variation does not depend on that of another (input, domain)
axis of symmetry
A vertical line that goes through the vertex of a quadratic function and divides the parabola into two congruent halves, that are mirror images of eachother(in𝑓 𝑥 =𝑎𝑥2 +𝑏𝑥+𝑐theaxisof symmetryis𝑥=− 𝑏) 2𝑎
area model
A visual model for multiplication; a rectangular array used to find all the factor pairs of a number or an expression
vertical line test
A way to test if a graph represents a function: if a vertical line drawn anywhere on a graph hits the graph in more than one place, then the graph is not a function since this shows an input value, 𝑥, has more than one output value, 𝑦
Shifting function
Adding or subtracting a constant to the independent variable of a function will shift the function left or right; adding or subtracting a constant to/from the dependent variable will shift the function up or down.
Natural Numbers
All positive integers greater than zero
Monomial
An algebraic expression consisting of one term
Polynomial
An algebraic expression consisting of one term or the sum of several terms that contain different powers of the same variable(s)
Trinomial
An algebraic expression consisting of three terms
Binomial
An algebraic expression consisting of two terms
Integers
Any positive or negative number, including zero but with no fractional or decimal part
Associative Property
Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication
skewed data
Data that have a long tail on one side or the other; a data set in which mean is greater or less than median
Mapping
Diagramming main ideas and connections between them.
Quartile
Divides a sorted data set into four equal parts, so that each part represents KP . Of the data set; 25% of the data within a data set.
Transformation
It occurs when an operation is performed on the dependent or the independent variable
whole numbers
Positive integers greater than or equal to zero; whole numbers cannot be negative or fractions
Division Property of Equality
Property of equality that is used to divide the same quantity into both sides of an equation, creating a different, but equivalent, equation
Multiplication Property of Equality
Property of equality that is used to multiply both sides of an equation by the same quantity, creating a different, but equivalent, equation
Subtraction Property of Equality
Property of equality that is used to subtract the same quantity from both sides of an equation, creating a different, but equivalent, equation
Negative Exponent Property
Property of equality that states that a number with a negative exponent should be moved to the other side of the fraction line and the exponent switched to positive
Addition Property of Equality
Property of equality that states that adding the same quantity to both sides of an equation creates a different (but equivalent) equation
Distributive Property
Property that states that multiplying a single term by two or more terms inside a set of parentheses yields an equivalent expression
Evaluating a function
Replace (substitute) a number for the function's variable; finding the value of the expression for that number
inverse function
Reverses or undoes the action of another function by interchanging the dependent and independent variables of the function for an appropriate set of values of the dependent variable
Power of a Product Property
States that if there is more than one factor in parenthesis, with an exponent outside the parenthesis, then the exponent is distributed to every term in the parenthesis
Power of a Quotient Property
States that the power of a quotient is equal to the quotient obtained when the dividend and divisor are each raised to the indicated power separately, before the division is performed
Product of Powers Property
States that the product of two powers with the same base is the base raised to the sum of the powers (exponents)
slope-intercept form
Takes the form of 𝑦 = 𝑚𝑥 + 𝑏 and represents the equation of a line with a slope of 𝑚 and and a 𝑦- intercept of 𝑏
average rate of change
The change in the value of a quantity divided by the elements in the interval or the elapsed time
Reflecting a function
The process of multiplying a function by negative one
inequality
The relation between two expressions that are not equal, " > " means greater than, and "<" means less than
domain
The set of values of 𝑥 used for the input of the function
range
The set of values of 𝑦 calculated from the domain or the output of the function
stander form of a quadratic
The sum of a quadratic term, a linear term, and a constantintheformof𝑦=𝑎𝑥2 +𝑏𝑥+𝑐
degree of a monomial
The sum of the exponents of all the variables of a monomial
output
The value of a function given a certain value for the known variable
Quotient of Powers Property
To divide powers with the same base, subtract their exponents
Power of a Power Property
To find a power of a power, multiply the exponents
compound inequality
Two or more inequalities that are connected by the words and or or.
Compressing a function
When a function is multiplied by a coefficient greater than zero but less than 1
linear function
When graphed, is a straight line that increases or decreases at a constant rate; the slope-intercept form of a linear function is 𝑦 = 𝑚𝑥 + 𝑏.
increasing interval
When reading a graph from left to right, as the 𝑥 values increase, the 𝑦 values increase
decreasing interval
When reading a graph from left to right, as the 𝑥 values increase, the 𝑦 values decrease
postitive slope
a postive function
root
a solution of an equation
interquartile range
is the middle 50% of the data set; includes the data points that lie between the first quartile the third one quartile; also known as IQR.
zeros
same as solutions , roots and x-intercept
1st quartile
the median of the lower half of the data set
3rd quartile
the median of the upper half of the data
real numbers
the set of all rational and irrational numbers
zero slope
the slope of a horizontal line
undefined slope
the slope of a vertical line
leading term
the term with the highest degree
