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Math Quiz 3 Cheat Sheet by

algebra     2     aglebra

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

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

Quadratic functions of the form

more parabolas


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

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


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

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

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

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

Quadratic Formula

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

Solving a Polynomial Inequality EX

Vertex Formula

Didn't go over


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