Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 3 - Linear and Quadratic Functions - 3.3 Quadratic Functions and Their Properties - 3.3 Assess Your Understanding - Page 146: 54



Work Step by Step

If the vertex of a graph is at $(m,n)$ then the vertex form for the quadratic function is $f(x)=a(x-m)^2+n$. According to the picture the vertex of the graph is at $(-2,6)$, hence the quardatic function becomes $f(x)=a(x+2)^2+6$. The point $(-4,-2)$ is on the graph, hence if we plug in the values we get: $-2=a(-4+2)^2+6\\-2=a(4)+6\\-8=4a\\a=-2$ Thus, the equation of the function is $f(x)=-2(x+2)^2+6$.
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