Common Core Algebra Regents Vocabulary

next term

f(n+1)

previous term

f(n-1)

What does a Quadratic Graph Look like

PARABOLA

equivalent

equal

Axis of Symmetry

x = -b / 2a; Axis of symmetry is ALWAYS an equation x = ____

Difference of Two Perfect Squares

x� - y�

Find algebraically

Need to show math steps to get your answer

To factor

To break a number or expression down into its multiplicative parts (unmultipy). For example you factor x^2 + 5x + 6 as (x+2)(x+3)

Definition of "to solve

To find the value of a variable that makes an equation true. For example you solve x - 2 = 4 by finding x = 6

equation of a vertical line

the equation of a vertical line is always x = a number such as x = -5

equation of a horizontal line

the equation of a vertical line is always y = a number such as y = -5

product

the result of multiplication; it can be helpful to use an area model to find the product of polynomials

sum

the result of addition

slope-intercept form of a line

y = mx + b; m is the slope and b is the y-intercept

standard form of a quadratic equation

y = ax� + bx + c

consecutive integers

x, x+1, x+ 2 (ex. 3,4,5)

consecutive odd integers

x, x+2, x+4 (ex 5,7,9)

consecutive even integers

x, x+2, x+4 (ex 6,8,10)

doubles/twice

multiplies by two; often a key word for exponential growth

expression

A mathematical statement with variables and constants but which does NOT contain any relation symbol (<,>,=,...)

equation

A mathematical statement with variables and constants which contains an equal sign

associative property

Sum or product of terms has the same value, regardless of how the terms are grouped. Example: 2x + (3 + y) = (2x + 3) + y

base

A number that is raised to a power

binomial

Polynomial with two terms Ex. (x + 4)

undefined fraction

A fraction whose denominator is equal to zero

coefficient

The numerical factor of a term in a polynomial. Example: 14 is the __________ in the term 14x

greatest common factor (GCF)

The greatest number, polynomial, or quantity that divides into two or more numbers or algebraic expressions evenly

commutative property

A property of real numbers that states that the sum or product of two terms is unaffected by the order in which the terms are added or multiplied; i.e., the sum or product remains the same. . Ex: 2x + y = y + 2x

coordinate pair

(x, y)

degree of a polynomial

The highest exponent value in the polynomial.

Conjugate Pairs

(a - b)(a + b)

distributive property

A property of real numbers that states that the product of a number and the sum or difference of two numbers is the same as the sum or difference of their products. Example: 2( 3 + x) = 2(3) + 2(x)

exponent

A number that tells how many times the base should be multiplied by itself

exponential decay

Represented by y = a(b^x) where a is the initial value and b is the growth factor.

exponential function

A function with a variable in the exponent. Outputs have a multiplication pattern.

exponential growth

A function where outputs have a multiplication pattern and the growth factor is greater than 1. (b>1)

factor (verb)

Break an expression into its multiplicative parts. "unmultiply

function

Each input (x) can only have one output (y)! Formally: A rule that assigns to each number x in the function's domain a unique number f(x) .

hypotenuse

The side of a right triangle opposite the right angle; the longest side of a right triangle. A key word for using the pythagorean theorem.

inequality

A mathematical statement containing one of the symbols <, >, ?,?,?to indicate the relationship between two quantities.

integers

{...-4, -3, -2, -1, 0, 1, 2, 3, 4, ... } (whole numbers both positive and negatives)

leading coefficient

The coefficient of the first term of a polynomial when the polynomial is in standard form. 5 is the leading coefficient of 5x�- 9x + 7

literal equation

An equation that contains more than one variable. Ex: 2a + 3y = c

monomial

A polynomial with one term.

mutliplication property of zero

For every number a, 0 � a = 0 and a � 0 = 0.

parabola

U shape made by a quadratic function

perimeter

Add up all the sides to find the length around a shape

binomial

A sum or difference of two unlike terms.

quadratic function

A function with an x� term

linear function

A function with a constant rate of change; often in the form y = mx + b

domain

All possible input values (x values)

range

All possible output values (y values)

real numbers

All the numbers on the number line (including fractions and decimals)

roots of an equation

A solution to an equation of the form f(x) = 0; find on a graph by looking at the x-intercepts OR by using factoring to solve OR by using the quadratic formula

slope

Constant rate of change: change in y over change in x

solution set

All solutions written in curley brackets Ex if x = 0 or x = -3 the solution set is x = {0,-3}

solution set of a system of inequalities

The solution set of a system of inequalities is a shaded REGION labeled S

solution set of a system of equations

The point where the equations intersect

solution to a system of equations/inequalities

(x,y) that satisfy all equations or inequalities

substitution

Method for solving systems of equations. Get a variable by itself and plug it into the other equation

elimination

Method for solving a system of equations. Add the equations that contain opposites together to get a variable to cancel out.

trinomial

A polynomial with three terms

recursive formula

Formula that tells how to get from one term of a sequence to the next term.

Arithmetic sequence

Sequence with a common difference. (adding or subtracting pattern)

Geometric sequence

Sequence with a common ratio.
(multiplying pattern)

y - intercept

Where a graph crosses the y-axis. This point will have an x- value of 0.

Slope intercept form of a line

y = mx + b where m is the slope and b is the y intercept

Standard form of a quadratic

y = ax� + bx + c; shows the y intercept of a parabola

compounded annualy

a key word for exponential growth

decays at a rate of

a key word for exponential decay

Factor completely

Make sure to look for the GCF to factor! Then continue the factoring procedure for the remaining polynomial.

Solution to a system of equations

Point(s) where two equations intersect

Solution to a system of inequalities

Shaded region where two inequalities intersect

Irrational numbers

Numbers that can't be written as a fraction... examples ?2 and ?

Rational numbers

numbers that can be expressed as fractions

Zeros of a graph

The x intercepts or solutions

nth term

a general formula for a sequence (hint... use the formulas on the reference sheet)

average rate of change

Slope or change in y over change in x

Cubic

A function with x raised to a power of 3

integers

{...-2,-1,0,1,2...} No decimals or fractions!

Average speed

another name for average rate of change; need to find change in distance divided by change in time

at least

?

at most

?

Slope Formula

Area of a Rectangle

Compound Interest Formula

A = P(1 + r)^t

How to change a decimal to a percent

Move the decimal point 2 places to the right

How to change a percent to a decimal

Move the decimal point 2 places to the left

Difference

to subtract

Quotient

to divide

Subtracted from/less than

switch order then subtract