Algebra 2 Final Formulas

sum of cubes

a³+b³=(a²-ab+b²

difference of cubes

a³-b³=a²+ab+b²

hyperbola

y=a/x-h +k (two curves in opposite corners)

hyperbola with a negative a

top left and bottom right

hyperbola with a positive A

top right and bottom left

direct variation

y=kx or k=y/x

inverse variation

y=k/x or k=xy

standard form

(x-h)²+(y-k)²=r²

equation for an ellipse

(x-h)²/rx²+(y-h)²/ry²=1

equation for hyperbola opening horizontally

(x-h)²/rx²-(y-h)²/ry²=1

ellipse

-(x-h)²/rx²+(y-k)²/ry²=1

parabola in vertex form

y=a(x-h)²+k

horizontally opening parabola

x=a(y-k)²+k

exponential function

y=a*b^x-h +k

exponential growth

when b>1

exponential decay

when 0<b<1

continuously compounded interest

A=Pe^rt

how can you rewrite y=log base b of x

b^y=x

lnx

log base e of x

if log bas b of x^n then…

n log base b of x

if log base b of b^n then…

n

if b to the power of log base b of n then…

n

Soh

Sin=opp/hyp

Cah

Cos=adj/hyp

Toa

Tan=opp/adj

hypotenuse of 30-60-90

2a

opposite of 60 in 306090

a times root 3

opposite of 30

a

hypotenuse of 45 45 90

a time root 2

opposites of 45 in 45 45 90

a

y=x

diagonal line

y=|x|

V-shaped graph

y=x²

U-shaped graph

y=x³

curve from either the bottom left to top right or bottom right to top left

y= square root of x

curve upward

y=2^x

exponential growth

y=log base 2 of x

start from bottom to top