absolute value

|n| is the distance from 0 to a number n on a number line. Ex |-3| = 3 and |5| = 5

next term

f(n+1)

previous term

f(n-1)

absolute value function

A function containing the |x|. It is shaped like the letter v

What does the graph of an Absolute Value Function Look Like

V or upside down V

What does a Quadratic Graph Look like

PARABOLA - The U shaped graph with a point(vertex) at the bottom or top.

What you do you know about the slopes of Parallel Lines

They are the same.

equivalent

equal

Axis of Symmetry

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

How do you factor the difference of two squares a^2 - b^2

(a - b)(a+b)

Find algebraically

Need to show math steps to get your answer

To factor

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

To Complete the square

means to rewrite as (x + ___)² + ____

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

What is the Line of Best Fit or Trend Line

It is the best line that can be drawn on a scatter plot that accurately represents the trend of the data.

What is a residual and when is a residual plot an indicator that you have a good model.

residual = actual - predicted; A residual plot indicates that a model is good when there is no pattern

What is the MODE in data

Most frequent number

What is the mean in data

It is the average

What is the median in data

Is is the middle number or average of the two middle numbers AFTER THEY ARE ARRANGED IN ORDER

Explain how to use the calculator to find the 5 numbers for a Box and Whisker plot

Hit STAT, then Edit and type in the values into L1. Once done hit STAT again -> to CALC and click on 1 Var Stats then scroll down to see the five number summary

RANGE of a data set

Maximum # - Minimum #

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

vertex form of a quadratic equation

y=a(x-h)² + k ; (h,k) is the vertex

standard form of a quadratic equation

y = ax² + bx + c ; a tells you whether the parabola opens up or down

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

multiplies by two; often a key word for exponential growth

f(x) + k

vertical (+ up/ -down) translation

f(x - k)

horizontal (+ left / - right) translation

expresion

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)

bivariate data

Data involving two seperate things being measured (Ex. height and age of a group of students)

box and whisker plot

closure

An operation is said to be closed if the output is the same type as the input. Example: Positive numbers are closed under addition because when you add two positive numbers the result is a positive number

coefficient

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

greatest common factor (GCF)

The greatest number, polynomial, or quantity that divides 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)

correlation

Measures how strong the relationship between two variables is

correlation coefficient

"r value"; between -1 and 1. The further away from zero, the stronger the relationship between the two variables are

cummulative frequency table

A table that shows how often each item, number, or range of numbers occurs in a set of data. This table displays the total number of scores that fall into each of several cumulative intervals. The cumulative intervals are created by adding the preceding tallies (of lower scores) to the new tallies for each interval.

degree of a polynomial

The highest exponent value in the polynomial.

difference of perfect squares

A binomial of the form a^2 - b^2 which can be factored into (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

expontial decay

An amount is multiplied by a number less than one every period time. Represented by y = a(b^x) where a is the initial value and b is the rate

exponential function

An function with a variable in the exponent. Has a multiplicative rate of change

exponential growth

An amount is multiplied by a number greater than one every period of time. Represented by y = a(b^x) where a is the initial value and b is the rate

factor (verb)

Break an expression into its multiplicative parts. "unmultiply"

five number summary

Minimum, 1st quartile, median, 3rd quartile, and maximum

frequency table

A table that shows how often each item, number, or range of numbers occurs in a data set.

function

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

histogram

A type of graph for 1 variable quantitative data. The horizontal axis is a number line that displays the data in equal intervals. The frequency of each bar is shown on the vertical axis.

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 5x²- 9x + 7

simplest radical form

Use factor tree to find the most simplified version of a square root

line of best fit

A line used to approximate and generalize the linear relationship between the independent and dependent variables for a set of data.

literal equation

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

mean

Another name for average. Add all the numbers and divide by how many there are (or get your calculator to do it for you!)

measure of central tendancy

"A summary statistic that indicates the typical value or center of an organized data set. The three most common measures of central tendency are the mean, an organized data set. The three most common measures of central tendency are the mean,

median

Middle value in a data set

mode

The most frequent number in a data set

monomial

A polynomial with one term (it has a coefficient and a variable)

mutliplication property of zero

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

parabola

U shape made by a quadratic function

parallel lines

Same slope different y intercept

perimeter

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

polynomial

A sum of monomials (2 or more terms)

proportional

Two variables are proportional if they maintain a constant rate of change and include the point (0,0)

quadratic function

A function with an x² term

linear function

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

quantitative

Descriptions using numerical measures such as quantity, height, or age.

qualitiative

Descriptions using word categories such as favorite color, type of eye color, or name

domain

All possible input values (x values)

range

All possible output values (y values)

right triangle

Go to your formula sheet and use the pythagorean theorem

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

scatter plot

Displays the relationship between two variables. DO NOT connect the lines

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 points 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 together to get a variable to cancel out.

trinomial

A polynomial with three terms

univariate

A data set involving one variable

vertex

The maximum or minimum point of a parabola

recursive function

Function that goes step by step. Start with f(1) then find f(2)...

axis of symmetry

x = -b/2a ; The x value in a vertex of a parabola

zero product property

If two terms multiplied equals zero, one of the terms equals zero; IE if ab=0 either a=0 or b=0

Quartile

Breaks a data set into 4 equal bins each with 25%

Arithmetic sequence

Sequence where the rate of change is additive; Look on your formula sheet for the general form

Geometric sequence

Sequence where the rate of change is multiplicative; Look on your formula sheet for the general form

Factored form

y = (x - 2)(x +3); shows the roots of a parabola

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 = ax² + bx + c; shows the y intercept of a parabola

Turning point

Another name for the vertex 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 GCF's to factor! Use slide divide bottoms up if the leading coefficient is still not equal to one after factoring out a GCF

Solution to a system of equations

Point(s) where two equations intersect

Solution to a system of inequalities

Shaded region where two inequalites intersect

Square root function

Function with a square root; use graphing calculator to visualize

Irrational numbers

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

Rational numbers

numbers that can be expressed as fractions

Vertical shift of a function

f(x) + k or f(x) - k

Horizontal Shift of a function

f(x - h) or f(x + h)

Vertical dilation (stretch) of a function

a f(x)

Residual

Actual value - predicted value; A linear model is a good fit if the graph of these is random

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)

Causal Relationship

Does one variable CAUSE the other variable. Remember, correlation doesn't mean causation!

Interquartile range

Q3 - Q1

average rate of change

Change in y over change in x; make a table using your graphing calculator to help!

Cubic

A function with x raised to a power of 3

Dot Plot

Number line with a dot for each data point above it

Where can I find the absolute value sign on my calculator?

Press the MATH button, scroll right to NUM and look for abs()

Where can I find cube roots on my calculator?

Press the MATH button and scroll down.

integers

...

Average speed

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