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: 53



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 $(1,-3)$, hence the quadratic function becomes $f(x)=a(x-1)^2-3$. The point $(3,5)$ is on the graph, hence if we plug in the values we get: $5=a(3-1)^2-3\\5=a(4)-3\\8=4a\\a=2$ Thus, the equation of the function is $f(x)=2(x-1)^2-3$.
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