College Algebra [5 ed.] 0495565210, 9780495565215
Learn to think mathematically and develop genuine problem-solving skills with Stewart, Redlin, and Watson's COLLEGE
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English Pages 789 Year 2008
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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