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 4 - Exponential and Logarithmic Functions - Cumulative Review - Page 373: 7

Answer

$2x^2-16x+24$

Work Step by Step

When the vertex of a graph is at $(h,k)$, then the general formula for the quadratic function is $f(x)=a(x−h)^2+k$. As depicted in the picture, the vertex of the graph is at $(h,k)=(4,-8)$ So, the quadratic function becomes: $f(x)=a(x−4)^2−8$. Since, the point $(0,24)$ is on the graph, plugging into the above equation gives: $24=16a-8 \implies a=2$ Thus, $f(x)=2(x−4)^2−8=2(x^2+16-8x)-8=2x^2-16x+24$
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