College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 4 - Section 4.3 - Quadratic Functions and Their Properties - 4.3 Assess Your Understanding - Page 299: 36

Answer

$a.\quad $see image $ b.\quad$ The domain is $(-\infty,\infty)$ The range is $[-\infty, 4)$ $ c.\quad$ Increasing on $(-\infty,2)$ Decreasing on $(2,\infty)$
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Work Step by Step

$f(x)=-x^{2}+4x$ $a=-1,b=4,c=0$ $ a.\quad$ Leading coefficient is negative - opens down. Vertex: $x=\displaystyle \frac{-b}{2a}=\frac{-(4)}{2(-1)}=+2$ $f(2)=-4+8=4$ Vertex: $(2,4)$ Axis of symmetry: the line $x=2$ Zeros $(x-$intercepts): $-x^{2}+4x=0$ $-x(x-4)=0$ $x=0$ or $x=4$ $x-$intercepts: $(0,0),(4,0)$ y-intercept: (0,c)$ = (0,0)$ $ b.\quad$ The domain is $(-\infty,\infty)$ The range is $[-\infty, 4)$ $ c.\quad$ Increasing on $(-\infty,2)$ Decreasing on $(2,\infty)$
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