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Complete cheat sheet for finel exam of college algebra
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Formula Sheet for College Algebra Final Exam
Properties of Exponents
p
p
mp
p np
m
n
n m p np mp
n m nm
nm m
n
n m nm
b
b
b
a
b
a
ab a b
a a
a a
a
a a a
−
−
Quadratic Formula
a
b b ac x 2
2 − ± − =
Circle
radius r
center hk
x h y k r
2 2 2
Vertex of Parabola
2
Vertex at h k
f x a x h k
a
b f a
b
Standard Form of Equation of Parabola
directrix x h p
focus h pk
vertex hk
y k p x h
directrix y k p
focus hk p
vertex hk
x h p y k
2
2
Properties of Logarithms
b p
b p
b
y x iff b x
p
b
p b
b
y b
b (^) =
log
log 1 0
log
log 1
log
m n
n
m
m n
mn
m p m
b b
b
b b
b
b
p b
log log
log log
log ( )
log log
ln( ) log ( )
log( ) log 10 ( )
a a
a a
= e
Change of Base Formula
b
x
b
x b x ln
ln
log
log log 10
10 = =
Properties of Radicals
b b
a
b
a
b b
a b ab
b b b
n n
n
m n mn
n n n
n
m n m n^ m
Absolute Value Inequalities
E k or E k
E k iff
E k iff k E k
Midpoint Formula
x 1 x 2 y 1 y 2 M
Distance Formula 2 2 1
2 d = ( x 2 −x 1 ) +(y −y)
Equations for Graphing Lines
1 1
2 1
2 1
y y mx x
y mx b x x
y y m
Interest Formulas
nt
n
r A P
compound
rt A Pe
continuous
=
Remainder Theorem: For any Poly. P(x), the remainder obtained when dividing P(x) by x - r is P(r).
Rational Root Theorem: Let (^10)
1 P( x) ax a 1 x ... ax a
n n
n = (^) n + + + +
− − , where all coefficients are
integers and n is a positive integer. If d
c is a root of P(x) then c is a factor of a 0 and d is a factor of an