Math 2B Algebra formulas reduced

Mathla maredu x the domain of log b x i s x 0 x 2 2ax

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Unformatted text preview: t; 0 x 2 + 2ax + a 2 = ( x + a ) n a a = n b b 1 n =a an nn b x log b = log b x logb y y 2 x 2 2 ax + a 2 = ( x a ) 2 b ± b 2 4 ac 2a If b 2 4ac > 0 - Two real unequal solns. If b 2 4ac = 0 - Repeated real solution. If b 2 4ac < 0 - Two compl ex so lutions. x= x 2 + ( a + b ) x + ab = ( x + a )( x + b ) x3 a 3 = ( x a ) ( x2 + ax + a 2 ) + ( y2 y1 ) ) = r log Quadratic Formula So lve ax 2 + bx + c = 0 , a 0 x3 + 3ax 2 + 3a 2 x + a 3 = ( x + a ) 2 b logb x = x Factoring Formulas x2 a2 = ( x + a ) ( x a ) Triangle I nequality ( x2 x1 ) r log b ( xy ) = log b x + logb y log x = log 10 x common log wher e e = 2.7 182818 28K d ( P , P2 ) = 1 an 1 = a n m = m n am a a na m = a n+ m lo g b ( x Special Logarithms ln x = log e x natural log Distance Formula If P = ( x1, y1 ) and P2 = ( x2 , y2 ) are two 1 points the distance between them is Exponent Properties log b b x = x Example log 5 125 = 3 because 53 = 125 Factoring and Solving a a = b b ab = a b Logarithm Properties log b b = 1 log b 1 = 0 x3 3ax2 + 3a 2 x a 3 = ( x a ) 3 3 Square Root Property If x2 = p t hen x = ± p x3 + a 3 = ( x + a ) ( x2 ax + a 2 ) Absolute Value Equations/Inequal ities If b is a positive number p =b p = b or p = b x2n a 2n = ( xn a n ) ( xn + a n ) If n is odd then, x n a n = ( x a ) ( x n1 + ax n 2 + L + a n 1 ) p <b = ( x + a)( x n 1 ax n 2 2 n 3 +a x L + a n 1 p < b or p>b ) Completing the Square (4) Factor the left side So lve 2 x 2 6 x 1 0 = 0 2 2 (1) Divide b y the coefficient of the x x 2 3x 5 = 0 (2) Move the constant to the other side. x 2 3x = 5 (3) Take half the coefficient of...
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This document was uploaded on 02/21/2014 for the course MATH 2B at UC Irvine.

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