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