Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.1 Polynomial Functions and Models - 3.1 Assess Your Understanding - Page 210: 114

Answer

$f(x)=-2 (x+4)(x+1)(x-2)$

Work Step by Step

Let us consider that $a$ is a zero of a function with multiplicity $b$. Then this factor of the function can be expressed as: $(x-a)^b$. Therefore, we can write the equation of the function as: $f(x)=k (x+4)(x+1)(x-2).(1)$ Since, $(0,16)$ lies on the graph, so we have: $k(4)(1)(-2) =16\\ -8k = 36 \\k=-2$ Thus, equation (1) becomes: $f(x)=-2 (x+4)(x+1)(x-2)$
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