Write all factors of p and q
Write the possible rational roots
Pick one and substitute it in, if you get 0, it is a factor
Divide out the factor using synthetic division

Back

Square Root Function

Front

2^√ (X)

Back

Rational Root Theorem

Front

+ We can see in the polynomial function to the right that of three possible roots (because the polynomial is of degree three) there are three real roots because it crosses the X-Axis three times. Furthermore, all three roots are rational because they cross clearly at integers. But what if we didn't have the graph provided?
+ We can find roots by factoring, but we don't know how to factor a

Back

Exponential Function

Front

X^x or e^x or 10^x

Back

Vertical Translation Down

Front

f (x) - #

Back

Cube Root Function

Front

3^√(X)

Back

Multiplying Powers

Front

For any real # a and positive integers m and n:
a^m * a^n = a^m+n

Back

Reflection Over Y-Axis

Front

f(-x)

Back

Standard Form

Front

f (x)= ax^2 +bx + c

Back

Factored Form the Vertex

Front

( x1 + x2/ 2 , f( x1 + x2/ 2))

Back

Vertex Form

Front

f (x)= a(b(x-h))^2 +k

Back

Square Roots

Front

For ant real # a and b, if a^2 = then a is a square root of b

Back

Vertical Translation up

Front

f (x) + #

Back

Linear Function

Front

f(x)= X

Back

Horizontal Translation Left

Front

f (x+ #)

Back

nth Root

Front

For any real # a and b any any positive integer n if a^n =b, then a is an nth root of b

Back

Quotient Property of Radicals

Front

For any real # a and b, b dose not =0, and any integer n, n>1,
n^√(a/b) = n^√(a) / n^√(b) if all roots are defined

Back

Log Function

Front

log(x)

Back

Absolute Value

Front

|x|

Back

Negative Exponents

Front

For any real # a, where a does not =0 and positive integers m and n:
a^-n = 1/ a^n and 1/ a^-n = a^n

Back

Quadratic Function

Front

X^2

Back

Horizontal Stretch

Front

b<1

Back

Vertical Compression

Front

a<1

Back

Horizontal Translation Right

Front

f (x - #)

Back

Finding a power of a Product

Front

For any real # a, b and positive integers m:
(ab)^m = a^m b^n

Back

Horizontal Compression

Front

b>1

Back

Vertex Form the formula for the Directrix

Front

y= k -1/4a

Back

Cube Function

Front

X^3

Back

Vertical Stretch

Front

a>1

Back

Factored Form the formula for Axis of Symmetry

Front

x= x1 + x2/ 2

Back

Raising a power to a power

Front

For any real # a, b and positive integers m:
(a^m)^n = a^mn

Back

Property of nth root

Front

For any real # a and and integer n > 1
1. if n is even, then n^√(a^n) =|a|
2. if n is odd, then n^√(a^n)= a

Back

Reflection over X- Axis

Front

-f(x)

Back

Rational function

Front

1/x

Back

Vertex Form the formula for the Focus

Front

( h, k + 1/4a)

Back

Logarithmic

Front

f (x) = log2 x

Back

Factored Form

Front

f (x)= a (x - x1) (x - x2)

Back

Product Property of Radicals

Front

For any real # a and b, b dose not 0 and integer n > 1
1. if n is even, then n^√(ab)= n^√a *n^√b when a and b are both nonnegative and
2. if n is odd, then n^√(ab) = n^√(a)* n^√(b)

Back

Diving Powers

Front

For any real # and integers m and n:
a^m/ a^n = a^m-n if a dose not =0