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: 33

Answer

$a.\quad $see image $ b.\quad$ The domain is $(-\infty,\infty)$ The range is $[-1,\infty)$ $ c.\quad$ Decreasing on $(-\infty,-1)$ Increasing on $(-1,\infty)$
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Work Step by Step

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