College Algebra 7th Edition

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

Chapter 1, Equations and Graphs - Section 1.2 - Graphs of Equations in Two Variables; Circles - 1.2 Exercises: 50

Answer

x-intercepts: $-3$ and $3$ y-intercept: $9$

Work Step by Step

RECALL: (1) A point where the graph touches or crosses the x-axis is called an x-intercept. Given an equation, the x-intercept/s can be found by setting $y=0$ then solving for $x$. (2) A point where the graph touches or crosses the y-axis is called a y-intercept. Given an equation, the y-intercept/s can be found by setting $x=0$ then solving for $y$. Solve for the x-intercept/s by setting $y=0$ then solving for $x$: $\begin{array}{ccc} &y &= &9-x^2 \\&0 &= &9-x^2 \\&0+x^2 &= &9-x^2+x^2 \\&x^2 &= &9 \\&x &= &\pm sqrt9 \\&x &= &\pm \sqrt{3^2} \\&x &= &\pm3 \end{array}$ The x-intercepts are $\pm 3$. Solve for the y-intercept/s by setting $x=0$ then solving for $y$: $\begin{array}{ccc} &y &= &9-x^2 \\&y &= &9-0^2 \\&y &= &9 \end{array}$ The y-intercept is $9$.
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