CLEP- College Algebra

#2

i^0 =

1

i^1 =

i

i^2 =

-1

i^3 =

-i

i =

square root of -1

square root of -25

5i

point-slope formula

y- y[one] =m(x - x[one])

find y-intercept

plug 0 in for x

find x-intercept

plug 0 in for y

quadratic formula

how many solutions are there when solving a quadratic formula

two; positive and negative options

inequality sign switch rule

switch sign when dividing OR multiplying [by] a negative number [not into]

how to solve for compound inequalities [ex. -3 < 2x - 1 < 5]

get x alone in the middle

difference of two squares

x^2 - a^2 = (x - a)(x + a)

difference of two cubes

x^3 - a^3 = (x - a)(x^2 + xa + a^2)

sum of two cubes

x^3 + a^3 = (x - a)(x^2 - xa + a^2)

sum of two squares

NOPE

perfect squares

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

perfect cubes

1, 8, 27, 64, 125

^3 square root of 8 --> can be written as

8^1/3

a^n * a^m =

a^n+m

a^n/a^m =

a^n-m

(a^n)^m =

a^n*m

a^-n =

1/a^n

1/a^-n =

a^n

(ab)^n =

a^n * b^n

(a/b)^n =

a^n/b^n

how to solve solve for quadratic roots

set equal to "0" or use quadratic formula

the two ways to solve a system of equations

substitution [solve for one variable at a time] & elimination [cancel out the same variables from each equation then solve for remaining variable]

Determinant/Cramer Formula

[ac{}bd] = ad - cb

how to solve if something is a function

if it passes the vertical line test

Vertical Line Test

if there are no same y values, then it is a function; if there are same y values, it is not a function

Domain

all the real numbers that go into a function; "x"

Range

all the real numbers that come out of a function; "y"

x = y^2

sideways parabola

a^n + a^m =

that's all folks

what does the discriminant tell

how many solutions a equation has

if discriminant is > 0

2 real solutions

if discriminant is = 0

1 real solution

if discriminant is < 0

0 real solutions; 2 imaginary solutions

discriminant

b^2 - 4ac

exponential function

y = b^x

inverse of b^x = y

x = b^y

switch log[2]8 = x

2^x = 8

switch log[3]81 = x

3^x = 81

switch log[4]32 = x

4^x = 32

if a set of points has repeating x values

then it is not a function

to find range

look for the smallest value possible

what to do for remainder question

find what x is equal to (of the divider equation) and then plug it into given equation

communicative property

switching order of numbers

associative property

to regroup numbers

what numbers are complex

all numbers are complex