College Algebra (10th Edition)

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

Chapter 2 - Section 2.2 - Graphs of Equations in Two Variables; Intercepts; Symmetry - 2.2 Assess Your Understanding - Page 166: 58


Intercepts: $(-9,0), (0,-3)$ and $(0,3)$. The graph has x-axis symmetry.

Work Step by Step

$\left[\begin{array}{ll} \text{x-intercepts:} & \text{y-intercepts:}\\ 0^{2}=-x+9 & y^{2}=0+9\\ x=9 & y^{2}=9\\ & y=\pm 3\\ & \end{array}\right]$ The intercepts are $(-9,0), (0,-3)$ and $(0,3)$. Test x-axis symmetry: Replace $y$ with $-y$ $(-y)^{2}=x+9$ $y^{2}=x+9$ ...same as initial equation Test y-axis symmetry: Replace $x$ with $-x$ $y^{2}=-x+9$ ... different from initial equation Test origin symmetry: $x\rightarrow-x$ and $y\rightarrow-y$. $(-y)^{2}=-x+9$ $y^{2}=-x+9$ ... different from initial equation
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