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