Title: Microsoft Word - Formula Sheet for College Algebra Final Exam.doc Author: cales Created Date: 5/2/2005 5:05:13 PM
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