algebra final

x^0 =

1

negative powers____

flip the thing

exponentials=exponentials can____

cancel out if they have the same base

log=log can___

cancel if they have the same log base

parent function points of a exponential function

(1,base)

(0,1)

(-1, 1/base)

parent function points for a logarithmic function

(base,1)

(1,0)

1/base,-1)

sum of cubes formula

a^3 + b^3 = (a+b)(a^2 - ab + b^2)

difference of cubes formula

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

odd positive end behavior

down, up

odd negative end behavior

up, down

even positive end behavior

up, up

even negative end behavior

down, down

x has a multiplicity of 1

cut through

x has a multiplicity of 2

bounce

x has a multiplicity of 3

flatten

how to find holes in a rational function

when factors cancel that is where the hole is located, then take number of hole and plug it back into your new equation

How to find the vertical asymptote of a rational function

set denominator equal to 0, x=___

how to find horizontal asymptote of a rational function

BOBO

BOTN

EATSDC

to compare the degree of the top and bottom of your equation

BOBO meaning

bigger on bottom = 0

BOTN meaning

bigger on top = none

EATSDC meaning

exponents are the same = divide coefficients

how to find the x-intercept of a rational function

set numerator equal to 0

how to find the y intercept of a rational function

plug in 0 for all the x's

circle conics equation

(x - h)² + (y - k)² = r²,

vertical ellipse equation

(x-h)^2/b^2 + (y-k)^2/a^2 = 1

horizontal ellipse equation

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

vertical parabola equation

y-k = a(x-h)^2

horizontal parabola equation

x-h = a(y-k)^2

how to find focal diameter length

I4pI

what does P stand for in parabola equations

the distance between the vertex and the focus, and the distance between the vertex and the directrix

how to solve for A or P in parabola equations

a=1/4p

SOAP

same opposite always positive, used for sum or difference of two squares.