Algebra and trigonometry, 2nd Edition

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EXPONENTS AND RADICALS x n  x mn x 1 x n  n x x n xn ayb  yn

x m x n  x mn 1x m2 n  x m n

1xy2 n  x n y n n

x1n  x n

x

n

mn

n

  x y xy

Rectangle

Box

A  l„ n

V  l„ h

P  2l  2„ m

n

n

mn

n m

m

x

x

n

Formulas for area A, perimeter P, circumference C, volume V :

 x  QxR n

y   y

   x    x  x m n

GEOMETRIC FORMULAS m

h

„ „ l

SPECIAL PRODUCTS 1x  y21x  y2  x  y 2

l

Triangle 2

A

1x  y22  x 2  2xy  y 2

Pyramid V  13 ha 2

1  bh 2

1x  y22  x 2  2xy  y 2

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

h

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

h a a

b

FACTORING FORMULAS

Circle

x 2  y 2  1x  y21x  y2

x  2xy  y  1x  y2 2

2

2

x  2xy  y  1x  y2 2

2

2

A  r2

V  43  r 3

C  2 r

A  4 r 2

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

r

x  y  1x  y21x  xy  y 2 3

3

2

Sphere

r

2

QUADRATIC FORMULA

Cylinder

Cone V  13  r 2h

V   r 2h

If ax 2  bx  c  0, then 2 b b   4ac x   2a

r h

h

INEQUALITIES AND ABSOLUTE VALUE

r

If a  b and b  c, then a  c. If a  b, then a  c  b  c. HERON’S FORMULA

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

means x  a

x  a

means x  a

B

a   s1 s a 21 s b 21 s c2

If a  0, then or

x  a.

means a  x  a. or

x  a.

abc where s   2

c A

a b

C

DISTANCE AND MIDPOINT FORMULAS

GRAPHS OF FUNCTIONS

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

Linear functions: f 1x2  mx  b

2 2 d   1x x y2 y 1  2 12  12 

y

x1  x2. , y1  y2. Midpoint of P1P2: a   b 2 2

y

b b

LINES

x

y2  y1 m   x 2  x1

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

Ï=b Power functions: f1x2  x n

y  y1  m 1x  x12

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

x y     1 a b

y

y

x x

Ï=≈

Ï=x£

f 1x2  x n

Root functions:

LOGARITHMS y  log a x

x

Ï=mx+b

y

y

means a y  x

log a a x  x

a log a x  x

log a 1  0

log a a  1

log x  log10 x

ln x  log e x

log a xy  log a x  log a y

log a axb  log a x  log a y y

log a x b  b log a x

log b x 

x

x

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Ï=œ∑ x

log a x log a b

Reciprocal functions: f1x2  1/x n y

y

EXPONENTIAL AND LOGARITHMIC FUNCTIONS y

y

y=a˛ a>1

x

x y=a˛ 0