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: 34

Answer

(a) See graph, opens down, vertex $(2,4)$, axis of symmetry $x=2$, intercept(s) $(0,0),(4,0)$. (b) domain $(-\infty,\infty)$, range $(-\infty,4]$. (c) decreasing on $(2,\infty)$, increasing on $(-\infty,2)$.

Work Step by Step

(a) See graph for $y=-x^2+4x=-(x-2)^2+4$, we can find that the graph opens down, vertex $(2,4)$, axis of symmetry $x=2$, y-intercept $(0,0)$, x-intercept(s) $(0,0),(4,0)$. (b) We can determine the domain $(-\infty,\infty)$, range $(-\infty,4]$. (c) The function is decreasing on $(2,\infty)$, increasing on $(-\infty,2)$.
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