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 2 - Linear and Quadratic Functions - Section 2.4 Properties of Quadratic Functions - 2.4 Assess Your Understanding - Page 158: 49


$f(x)=2(x -1)^2-3$

Work Step by Step

The vertex form of the quadratic function $ax^2+bx+c=0$ can be expressed as $f(x)=a(x-h)^2+k$ and its vertex is at $(h, k)$. As depicted in the picture, the vertex of the graph is at $(h, k)=(1,-3)$, and thus, the quadratic function becomes $f(x)=a(x -1)^2-3$. Plug in the values $(3, 5)$ to obtain: $5=a(3-1)^2 - 3 \\ 4a=8 \implies a=2$ Therefore, the equation of the function can be expressed as: $f(x)=2(x -1)^2-3$
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