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Unformatted text preview: Important Formulas for Test 1 Material Instructor: Ms. Hoa Nguyen ([email protected]) • Quadratic function: – f ( x ) = a ( x h ) 2 + k has the vertex ( h, k ). – If a > 0, parabola opens UP ⇒ vertex = MINIMUM (AT xvalue, OF yvalue). – If a < 0, parabola opens DOWN ⇒ vertex = MAXIMUM (AT xvalue, OF yvalue). – The vertex of f ( x ) = ax 2 + bx + c is computed: x = b 2 a , y = f ( x ). • The zeros of a quadratic function f ( x ) = ax 2 + bx + c can be computed by QUADRATIC formula: x = b ± √ b 2 4 ac 2 a . • Power function f ( x ) = x n : Notice : Use the graph of the power functions to look at the end behavior of a polynomial in such a question as “select the polynomial equation of the given graph” (Questions 15, 16 in Review Set of Test 1 Material: Part 1). • Polynomial f ( x ) = a n x n + a n 1 x n 1 + ... + a 1 x + a : – The POWERs of x are NATURAL numbers, i.e., * NO NEGATIVE (for example, 5 x 2 = 5 x 2 ). * NO FRACTION (for example, x 1 3 ). * Notice : f ( x ) = 2 x 4 5 is a polynomial because the power of x is a NATURAL number 4, and f ( x ) = 2 5 x 4 5 satisfies the above form. – The DEGREE of a polynomial is the HIGHEST POWER of x . For example, f ( x ) = x ( x 2 +4)( x 5) 2 has DEGREE 5 because the highest term is x · x 2 · x 2 = x 5 ⇒ HIGHEST POWER = 5 = DEGREE of f ....
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This note was uploaded on 05/23/2011 for the course MAC 1147 taught by Professor Nuegyen during the Spring '11 term at FSU.
 Spring '11
 Nuegyen
 Formulas

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