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Math Quiz 3 Cheat Sheet by

Parabola f(x)= a(x-h) 2

h determines x axis
( 2 negatives= positive)
If a is positive parabola is up or to the right
Vertex is at (h,k)
if a is negative opens left or down
(x-3)2 -5 -->
move to the right
If parent­hesis is addition, move to the left

Graph the functions. Plot at least 3..

Make a table for eqaution
pick points for x
graph answers
should be in the form of f(x)=bx

Graph the functions. plot at least.. (Rules)

if b>1 its a expone­ntial growth function
if 0<b­<1 its a expone­ntial decay function
if b>1 Domain = (- infinity, infinity)
if b>1 Range = (0,inf­inity)
if b>1The line y=0 is horizontal asympote
if b>1 Function passes through (0,1)

Solve. ax +bx+c=0

more parabolas

Quadratic functions of the form

Shifting Parabolas

f(x) = ax2+bx+c is a parabola
f(x)= x2+k
f(x)= (x-h)2
a>0 opens up
is a vertical shift of f(x)=x^2
h>0 shifted right vice versa
a<0 opens down
k>0 shifted up vice versa

x (possible extra terms here)= square root of b

Steps: get it in the form of the equation by adding and subtra­cting different sides
Apply sqaure root and the plus or mins sign

Find the inverse

Change f(x) to y
Switch x & y
Solve for y
Don't forget about cross multip­lying


log 1=1
Only solve multiple logs if they have the same base
log bx =x
log (xy) = log (x) + log (y)
blog sub bx =x
log 1=0
log b=1
power is what it's equal to
base is the sub

Solve log equation.

Convert to expone­ntial form based off of note
23= 8 which is log 8 = 3

Solve using Substi­tution.

Substitute the same terms with a letter
Solve for the letter ex: (x=2)
Replace the letter with what was in the equation

Solve the inequality using the test point method


Didn't go over


Vertex Formula

Solving a Polynomial Inequality EX

Solving a Polynomial Inequality

Think of it as a Quadratic equation (< OR > as a = sign)
Solve equation
Plot answers
Pick numbers from each A,B,C
if equation is tue part of solution
if false not part of solution
find and write out solution set

Quadratic Formula

Solve the equation b = c

Get bases same by putting a power or square root or fraction
Cross out bases
Exponents become base
Solve equation
Sometimes doesnt look like example, general it has 2 numbers raised to a power with an equal sign between

Graphing inverse

Look at > or < sign, determines what part of parabolas are the answer
Find the inverse
plot parabola from solved equation "­y=..."
Make a table of points

f and g functions

replace f and g perform operation in middle
Horizontal line test
(g ∘ f )(x) = g(f(x))
intersects more than once, not a function


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