College Algebra, 5th Edition

EXPONENTS AND RADICALS

1x 2
x

mn

1xy2
x y n

n n

n

n

n

n

Midpoint of P1P2:

n m

a

x1  x2 y1  y2 , b 2 2

n

LINES

n

1xy
1x 1y m

d
21x2  x1 2 2  1y2  y1 2 2

x m/n
1x m
A 1xB m

n

x 1/ n
1x n

Distance between P11x1 , y12 and P2 1x 2 , y2 2:

xm
x mn xn 1 x n
n x x n xn a b
n y y

x m x n
x mn m n

DISTANCE AND MIDPOINT FORMULAS

x 1x
n By 1y n

mn

2 1x
2 1 x
1 x

Slope of line through P11x1 , y12 and P2 1x 2 , y2 2

m


y  y1
m1x  x12

Point-slope equation of line through P11x1, y12 with slope m

SPECIAL PRODUCTS 1x  y21x  y2
x 2  y 2

1x  y22
x 2  2xy  y 2 1x  y22
x 2  2xy  y 2

1x  y23
x 3  3x 2 y  3xy 2  y 3 1x  y23
x 3  3x 2 y  3xy 2  y 3

Slope-intercept equation of line with slope m and y-intercept b

y
mx  b

Two-intercept equation of line with x-intercept a and y-intercept b

y x 
1 a b

The lines y
m 1x  b1 and y
m 2x  b2 are Parallel if the slopes are the same

m1
m2

Perpendicular if the slopes are negative reciprocals

m 1
1/m 2

FACTORING FORMULAS x 2  y 2
1x  y21x  y2

x 2  2xy  y 2
1x  y22 x 2  2xy  y 2
1x  y22

LOGARITHMS

x 3  y 3
1x  y21x 2  xy  y 2 2

log a a x
x

a log a x
x

log a 1
0

log a a
1

x 3  y 3
1x  y21x 2  xy  y 2 2

y
log a x means a y
x

QUADRATIC FORMULA Common and natural logarithms If ax 2  bx  c
0, then

log x
log10 x

b  2b2  4ac x
2a

Laws of logarithms log a xy
log a x  log a y

INEQUALITIES AND ABSOLUTE VALUE If a  b and b  c, then a  c. If a  b and c  0, then ca  cb.

Change of base formula log a x logb x
log a b

If a  b and c  0, then ca  cb. If a  0, then

or

0x0 a

or

x
a.

0 x 0  a means a  x  a. means x  a

x loga a b
loga x  loga y y log a x b
b log a x

If a  b, then a  c  b  c.

0 x 0
a means x
a

y2  y1 x2  x1

x  a.

ln x
log e x

Exponential functions: fÓxÔ
ax

GRAPHS OF FUNCTIONS

y

Linear functions: f1x2
mx  b y

y

Ï=a˛ a>1

y

Ï=a˛ 0