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 157: 9



Work Step by Step

The coordinates of the vertex of a quadratic function $f(x) = ax^2+bx+c$ are given by: $\displaystyle(\frac{-b}{2a}, f(-\frac{2}{a}))$ We see that the given quadratic function has the coefficients: $a=-1, b=4, c=5$. Therefore, the coordinates of the function's vertex can be expressed as: $(-\dfrac{4}{2\cdot(-1)}, f(-\dfrac{4}{2\cdot(-1)}))=(-\dfrac{4}{-2}, f(-(-2)) \\=[2, f(2)]$ So, the vertex has a y-coordinate of $f(2)$. Therefore, the given statement is $\bf{True}$.
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