College Algebra [4 ed.] 0534405991, 9780534405991

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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