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formula memorization sheet Material Type: Notes; Professor: Bolin; Class: Precalculus I; Subject: Mathematics; University: Lansing Community College;
Typology: Study notes
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Properties of Exponents
a (^) a a
a bn^ m r anr bmr
n r nr m mr
a a b b
Quadratic Formula ^ ^2 ^4 2 x b^ b^ ac a
Vertex of Parabola (^) ^
b (^) f b a a f x ( ) a x( h) 2 k Vertex at( ,h k )
Circle ( x h) 2 ( y k) 2 r^2
center ( ,h k ) radius r
Properties of Logarithms
Change of Base Formula 10 10
log log^ ln b log ln x x^ x b b
Properties of Radicals
m (^) n m^ m n (^) b b bn
n n^ a^ na^ b b b
Distance Formula
M x^ x^ y^ y
Equations for Graphing Lines
2 1 2 1
m y^ y , y mx b x x
Exponential Growth Model: P t( ) P e 0 kt Doubling Time: T ln 2 k Exponential Decay Model: P t( ) P e 0 kt Half Life: T ln 2 k
Special Product Formulas
Sum or Difference of Cubes
Absolute Value Inequalities E k iff k E k E k iff E k or E k
(^) Interest Formulas Compound ^
r^ nt A P n Continuous A Pert
Remainder Theorem: For any polynomial P x( ), the remainder obtained when dividing P x( )by x r is P r( ).
Rational Root Theorem: Let P x( ) a xn n an (^) 1 xn ^1 a x 1 a 0 , where all coefficients are
integers and n is a positive integer. If c d is a root of P x( )then c is a factor of a 0 and dis a factor an.
Note: Students are not allowed to use this formula sheet during any tests or final exams.