College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises: 6

Answer

(a) vertex: $(-2, 8)$ x-intercepts: $-6$ and $2$ y-intercept: $6$ (b) maximum value: $8$ (c) domain: $(-\infty, +\infty)$ range: $-\infty, 8]$

Work Step by Step

RECALL: (a) The parabola opens downward so the vertex is the maximum point of the graph. Thus, the vertex is $(-2, 8)$ The graph clearly shows that the x-intercepts are $-6$ and $2$ while the y-intercept is $6$ (b) The parabola opens downward so the function has a maximum value, which is the y-coordinate of the vertex. Thus, the maximum value if $f$ is $8$. (c) The domain of a quadratic function is the set of all real numbers, $(-\infty, +\infty)$ The y-values of the function are from $8$ and below. Thus, the range is $(-\infty, 8]$.
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