Algebra

Question 1

Identities

(a + b)²

Answer 1

a² + 2ab + b²

Question 2

Identities

(a-b)³

Answer 2

a³ - 3a²b + 3ab² - b³

Question 3

Identities

a² - b²

Answer 3

(a + b) (a - b)

Question 4

Exponent Rules

X^-a

Answer 4

1

x^a

Question 5

Exponent Rules

(x^a)(x^b)

Answer 5

x^a+b

Question 6

Exponent Rules

x^a

x^b

Answer 6

x^a-b

1

x^b-a

(if negative)

Question 7

Exponent Rules

x⁰

Answer 7

1

Question 8

Exponent Rules

0⁰

Answer 8

not defined

Question 9

Exponent Rules

(x^a)(y^a)

Answer 9

(xy)^a

Question 10

Exponent Rules

(x/y)^a

Answer 10

x^a/y^a

Question 11

Exponent Rules

(x^a)^b

Answer 11

x^ab

Question 12

2 ways to solve linear equations with 2 variables

Answer 12

Substitution

Elimination

Question 13

Quadratic equation form

Answer 13

ax² + bx + c

Question 14

Quadratic formula

Answer 14

x= -b+/- √(b²- 4ac)

2a

Question 15

√-x

Answer 15

undefined

Question 16

Factoring a quad equation when answer = 0

Answer 16

Factor into parentheses and set each as equal to zero since the answer is zero

Yields two possible answers

Question 17

Solution set

Answer 17

all the values that can make an inequality true

Question 18

Equivalent inequalities

Answer 18

have the same solution set

Question 19

Inequalities:

multiplying or dividing by a negative

Answer 19

Reverse direction of the symbol

Question 20

State inequality solution x >/= 4

Answer 20

all real numbers greater than or equal to 4

Question 21

Distance formula

Answer 21

d = rt

rate

time

Question 22

Domain of a function

Answer 22

all permissable values of the variable

Question 23

Simple interest formula

Answer 23

V = P R T

Value
Principle

rate % in decimal form

time (years)

Question 24

Compound interest formula (annual)

Answer 24

V = P (1 + r/100)^t

Question 25

Compound interest formula (other time intervals)

Answer 25

V = P(1+ r/100n)^nt

n times per year

t years

Question 26

P(x,y) and P¹(x,-y)

Answer 26

symmetric/reflect about the x axis

Question 27

P(x,y) and Pⁿ(-x,y)

Answer 27

Symmetric/reflect about the y axis

Question 28

P(x,y) and P^m(-x, -y)

Answer 28

symmetric/reflect about the origin

Question 29

How to find the distance between two points using the Pythagorean theorem

Answer 29

1. Construct a right triangle
2. Fing lengths of shorter sides (subtract whichever numbers differ, x¹-x² or y¹-y²)
3. Apply theorem

Question 30

What does the graph of an equation (with 2 vars) show

Answer 30

all points whose ordered pairs satisfy the equation

Question 31

How to find the slope of a line that passes through 2 points

Q(x₁,y₁) and R(x₂,y₂)

Answer 31

y₂-y₁ / x₂-x_{1 = m}

rise/run

Question 32

slope = 0

Answer 32

horizontal line, no rise

Question 33

equation for horizontal lines

Answer 33

y=b

Question 34

vertical slopes

equation

Answer 34

not defined

x = a (x-intercept)

Question 35

When slopes are equal, the lines are

Answer 35

parallel

Question 36

When one slope is the negative reciprocal of the other (i.e 2 and -1/2)

Answer 36

the lines are perpendicular to each other

Question 37

How to find the x-intercept from a y=mx+b equation

Answer 37

set y=0

solve for x

Question 38

how to find a graph solution with a system of equations

Answer 38

solve for y in terms of x

graph

solution is where the 2 lines intersect

Question 39

How to find a graph solution for a system of linear inequalities

Answer 39

solve for y in terms of x

shade regions

solution of the set are all points that fall in shaded regions

Question 40

describe line y = x

Answer 40

passes through origin

slope of 1

makes 45 degree angle with each axis

Question 41

how points (a, b) and (b, a) relate

Answer 41

reflect across the line y=x

Question 42

Describe what a quadratic equation looks like on a graph

Answer 42

parabola

symmetric about line through vertex

the two x-intercepts are equidistant from the vertex line

Question 43

ax² + bx + c = 0

if a is positive…

if a is negative…

Answer 43

parabola opens upward and vertex is lowest point

opens down and vertex is highest

Question 44

(x - a)2 + (y - b)2 = r2 form

Answer 44

circle

center is (a, b)

radius is r

Question 45

Graphing functions

Answer 45

x is input

y= f(x)

f(x) = mx + b….y = mx + b

Question 46

how to find the intersection points of two functions

Answer 46

1. set the functions as equal to each other [g(x) = f(x)]
2. Solve for x with quadtractic equation form
3. Quadratic formula - results are x coordinates
4. Plug in each result into one of the functions to find coresponding y coordinates

Question 47

Graph of a function of an absolute value

Answer 47

V-shaped

y= x and y= -x

join at the origin

Question 48

Graph of functions with square root/ negative square root

Answer 48

half parabolas

right and left half reflections of y= x² about the y= x line

Question 49

y = -h(x) and y = h(x)

Answer 49

-h(x) is the reflection of h(x) about the x-axis

Question 50

h(x) + c

Answer 50

h(x) shifts up c units

Question 51

h(x) - c

Answer 51

h(x) shifts down c units

Question 52

h(x+c)

Answer 52

h(x) shifts left c units

Question 53

h(x-c)

Answer 53

h(x) shifts right c units

Question 54

ch(x)

c > 1

Answer 54

h(x) stretched vertically by a factor of c

Question 55

ch(x)

0 < c < 1

Answer 55

h(x) shrunk vertically by factor of c

Question 56

Formula for circles on xy plane

Answer 56

(x - a)2 + (y - b)2 = r2

Question 57

X^a/b

Answer 57

^b√x^a