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