Formula Sheet for College Algebra Final Exam

Formula Sheet for College Algebra Final Exam Quadratic Formula

Properties of Exponents

1. a a = a n

m

n+m

x=

n

a 2. m = a n − m a 3. (a n ) m = a nm

6. b − p

− b ± b − 4ac 2a

( x − h) 2 = 4 p ( y − k ) vertex = (h, k )

Circle

4. (a n b m ) p = a np b mp  an 5.  m b

Standard Form of Equation of Parabola

2

p

( x − h) 2 + ( y − k ) 2 = r 2 center = (h, k ) radius = r

 a np  = mp b  1 = p b

focus = (h, k + p ) directrix : y = k − p ( y − k ) 2 = 4 p ( x − h)

Vertex of Parabola

 − b  − b   , f    2 a  2a   f ( x ) = a ( x − h) 2 + k

vertex = (h, k ) focus = (h + p, k ) directrix : x = h − p

Vertex at (h, k ) Properties of Logarithms

1. y = log b x iff b = x y

2. log b b = 1

5. b logb p = p m

E ≤ k iff

m n

n

3.

m n n

a

n

b

E ≤ −k

b = mn b =n

a ,b ≠ 0 b

−k ≤ E ≤ k

E ≥ k iff

a n b = n ab

2.

4.

= n bm = b

10. ln(a) = log e (a )

Absolute Value Inequalities

Properties of Radicals n

7. log b (mn) m 8. log b   n = log b m − log b n

4. log b 1 = 0

( b)

9. log(a) = log10 (a)

= log b m + log b n

3. log b b p = p

1.

6. log b m p = p log b m

or

E≥k

Midpoint Formula

 x + x 2 y1 + y 2  , M = 1  2   2

Change of Base Formula

log b x =

log10 x ln x = log10 b ln b

Distance Formula

d = ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2 Equations for Graphing Lines

m=

y 2 − y1 , y = mx + b x 2 − x1

y − y1 = m( x − x1 )

Interest Formulas

compound  r A = P 1 +   n continuous

nt

A = Pe rt Remainder Theorem: For any Poly. P(x), the remainder obtained when dividing P(x) by x - r is P(r). Rational Root Theorem: Let P ( x ) = a n x + a n −1 x n

integers and n is a positive integer. If

n −1

+ ... + a1 x + a 0 , where all coefficients are

c is a root of P(x) then c is a factor of a 0 and d is a factor of a n d