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: 8


vertex: $(-1, 0)$ axis of symmetry: $x=-1$ minimum value: $0$ range: $y\ge0$

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 prarabola. Notice that the vertex is at $(-1, 0)$. 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 $x=-1$. The parabola opens downward so the $y$-coordinate of the vertex is the minimum value. Hence, the minimum value is $0$. The values of the function are all greater than or equal to zero. Thus, the range is $y\ge0$.
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