College Algebra [4 ed.] 0534405991, 9780534405991

James Stewart, author of the worldwide, best-selling Calculus texts, along with two of his former Ph.D. students, Lothar

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College Algebra [4 ed.]
0534405991, 9780534405991

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James Stewart
Lothar Redlin
Saleem Watson

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EXPONENTS AND RADICALS

DISTANCE AND MIDPOINT FORMULAS

am amn an 1 an n a n an a n b b

aman amn ÓamÔn amn

Distance between P1Ó x 1, y 1Ô and P2Ó x 2, y 2Ô: 2 2 y d œÓ x x Ó y 2 1Ô 2 1Ô

Midpoint of P1 P2:

!@

ÓabÔn anbn a1n œn a

!œn a @ a mn œn am

2

1

2

m

œa a b œn b

n

1

LINES

n

œn b œn ab œn a

x x y y , @ ! 2 2

œm œn a œn œm a mœn a SPECIAL PRODUCTS ÓA BÔ2 A2 2AB B2

y2 y1 m x2 x1

Slope of line through P1Óx 1, y 1Ô and P2Óx 2, y 2Ô Point-slope equation of line through P1Óx 1, y 1Ô with slope m

y y 1 mÓ x x 1Ô

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

y mx b x y 1 a b

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

ÓA BÔ2 A2 2AB B2 ÓA BÔ3 A3 3A2B 3AB2 B3

The lines y m1 x b1 and y m 2 x b 2 are

ÓA BÔ3 A3 3A2B 3AB2 B3 FACTORING FORMULAS A2 B 2 ÓA BÔÓA BÔ

Parallel if the slopes are the same

m1 m2

Perpendicular if the slopes are negative reciprocals

m1 1m2

A2 2AB B2 ÓA BÔ2

LOGARITHMS

A2 2AB B2 ÓA BÔ2

y loga x

means a y x

A3 B 3 ÓA BÔÓA2 AB B2Ô

loga a x x

aloga x x

A B ÓA BÔÓA AB B Ô

loga 1 0

loga a 1

3

3

2

2

QUADRATIC FORMULA

Common and Natural Logarithms ln x loge x

log x log10 x

If ax 2 bx c 0, then a b œ b 2 4 c x 2a INEQUALITIES AND ABSOLUTE VALUE If a b and b c, then a c.

Laws of Logarithms loga AB loga A loga B A loga loga A loga B B

! @

loga AC C loga A

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

Change of Base Formula

If a b and c 0, then ca cb.

loga x logb x loga b

If a 0, then x a

means x a

x a

means a x a.

x a

means x a

or

or

x a. x a.

SOME FUNCTIONS AND THEIR GRAPHS

y

y

y

fÓxÔ mx b

Linear functions

fÓxÔ ax

Exponential functions

Ï=a˛ a>1

y

Ï=a˛ 0