Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-2 Standard Form of a Quadratic Function - Practice and Problem-Solving Exercises - Page 206: 13

Answer

vertex: $\left(-0.75, 5.125\right)$ axis of symmetry: $x=-0.75$ maximum value: $5.125$ range: $y\le 5.125$

Work Step by Step

Use a graphing utility to graph the given function. Refer to the graph below. The vertex is the lowest or highest point on the parabola. Notice that the vertex is at $\left(-0.75, 5.125\right)$. The axis of symmetry of the graph is the line $x=h$ where $h$ is the $x$-coordinate of the vertex. Thus, the axis of symmetry is $x=-0.75$. The parabola opens downward so the $y$-coordinate of the vertex is the maximum value. Hence, the maximum value is $5.125$. The values of the function are all less than or equal to $5.125$. Thus, the range is $y\le 5.125$. vertex: $\left(-0.75, 5.125\right)$ axis of symmetry: $x=-0.75$ maximum value: $5.125$ range: $y\le 5.125$
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