Advanced Algebra 2 Formulas

Front 1

Natural numbers/counting numbers (N)

Back 1

{1,2,3...}

Front 2

Whole numbers (W)

Back 2

{0,1,2...}

Front 3

Integer numbers (Z)

Back 3

{...-2,-1,0,1,2...}

Front 4

Rational numbers (Q)

Back 4

Can be express in form m/n where m and n are real numbers and n is not equal to 0 (terminating or repeating decimals)

Front 5

Irrational numbers (I)

Back 5

All non-terminating or non-repeating decimals

Front 6

Real numbers (R)

Back 6

All rational and irrational numbers

Front 7

Closure Property

Back 7

a+b is a real number; ab is a real number

Front 8

Commutative Property

Back 8

a+b=b+a; ab=ba

Front 9

Associative Property

Back 9

(a+b)+c=a+(b+c); (ab)c=a(bc)

Front 10

Identity Property

Back 10

a+0=a; a*1=a

Front 11

Inverse Property

Back 11

a+(-a)=0; a*(1/a)=1

Front 12

Distributive Property

Back 12

a(b+c)=ab+ac

Front 13

Opposite Numbers

Back 13

Two numbers that are the same distance from the origin on a number line but on different sides

Front 14

How to find the x-intercept

Back 14

Set y=0 and solve for x

Front 15

How to find the y-intercept

Back 15

Set x=0 and solve for y

Front 16

Slope Intercept Form

Back 16

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

Front 17

Standard Form

Back 17

ax+by=c

Front 18

Absolute Value Graphs

Back 18

y=|x|+b, where b shifts the graph up or down that many units; y=|x+b|, where b shifts the graph left or right that many units (in opposite direction)

Front 19

Find the vertex of an absolute value equation

Back 19

1. Set the expression in the absolute value bars equal to 0 and solve for the variable. It will represent the x value.
2. Plug the x value into the original equation to find a point.

Front 20

What does f(x) mean?

Back 20

y=

Front 21

Domain

Back 21

The set of all numbers that allow a function to be defined (x values)

Front 22

Range

Back 22

The set of all numbers that are y values of a function

Front 23

To solve for a domain:

Back 23

1. If there is a variable in the denominator, set the denominator not equal to 0 and solve for x.
2. If there is a square root, set the expression under the square root greater than or equal to 0 and solve for x.
3. If there is a square root in the denominator, set the expression greater than 0 and solve for x.
4. In most other cases, the domain is the set of real numbers.

Front 24

To solve for range:

Back 24

Solve the function for x and use the same procedure as you would for finding the domain.

Front 25

Linear Programming

Back 25

Goal is to find optimization value. Use vertices to determine the maximum or minimum value of the objective quantity

Front 26

Steps to finding the maximum or minimum objective quantity

Back 26

1. Graph the system in order to determine the variables.
2. Evaluate the objective quantity at each vertex.
3. Not all objective quantities will have both a maximum and a minimum.

Front 27

Matrices

Back 27

Written as rows by columns, or M x N

Front 28

Determinate |A|

Back 28

Use your calculator

Front 29

Compound Interest

Back 29

A=P(1+(r/n))^NT
A – the amount in bank after T years
P – principle (initial amount), also A0
R – interest rate (decimal)
N – number of time compounded per year
T – how many years