Formula Sheet for College Algebra Final Exam
Properties of Exponents
p
p
mp
np
p
m
n
mpnppmn
nmmn
mn
m
n
mnmn
b
b
b
a
b
a
baba
aa
a
a
a
aaa
1
.6
.5
)(.4
)(.3
.2
.1
=
=
=
=
=
=
−
−
+
Quadratic Formula
a
acbb
x2
4
2−±−
=
Circle
rradius
khcenter
rkyhx
=
=
=−+−
),(
)()( 222
Vertex of Parabola
),(
)()(
2
,
2
2
khatVertex
khxaxf
a
b
f
a
b
+−=
−−
Standard Form of Equation of
Parabola
phxdirectrix
kphfocus
khvertex
hxpky
pkydirectrix
pkhfocus
khvertex
kyphx
−=
+=
=
−=−
−=
+=
=
−=−
:
),(
),(
)(4)(
:
),(
),(
)(4)(
2
2
Properties of Logarithms
pb
pb
b
xbiffxy
p
b
p
b
b
y
b
b=
=
=
=
==
log
.5
01log.4
log.3
1log.2
log.1
nm
n
m
nm
mn
mpm
bb
b
bb
b
b
p
b
loglog
log.8
loglog
)(log.7
loglog.6
−=
+=
=
)(log)ln(.10
)(log)log(.9 10
aa
aa
e
=
=
Change of Base Formula
b
x
b
x
x
bln
ln
log
log
log
10
10 ==
Properties of Radicals
()
0,.4
.3
.2
.1
≠=
=
=
==
b
b
a
b
a
bb
abba
bbb
n
n
n
mn
mn
nnn
n
m
nm
m
n
Absolute Value Inequalities
kEorkE
iffkE
kEkiffkE
≥−≤
≥
≤≤−≤
Midpoint Formula
++
=2
,
2
2121 yyxx
M
Distance Formula
2
12
2
12 )()( yyxxd −+−=
Equations for Graphing Lines
)(
,
11
12
12
xxmyy
bmxy
xx
yy
m
−=−
+=
−
−
=
Interest Formulas
nt
n
r
PA
compound
+= 1
rt
PeA
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 01
1
1...)( axaxaxaxP 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 0
a and d is a factor of n
a