Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Test - Page 101: 22

Answer

The graph of the equation $y=x^{2}-4$ is a parabola that opens upward with points $(0,-4), (2,0)\: and \:(-2,0)$.
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Work Step by Step

$$y=x^{2}-4$$ The best way to graph the equation is to find the intercepts by alternately setting the value of $x$ and $y$ to $0$. Thus, to get the $y-intercept$: $$y=x^{2}-4$$ $$ y=0^{2}-4$$ $$y= -4$$ To get the $x-intercept$ $$ y=x^{2}-4$$ $$ 0=x^{2}-4$$ Add $4$ to both sides. $$ 0+4=x^{2}-4+4$$ $$ 4=x^{2}$$ Get the squareroot of both sides $$\sqrt 4 = \sqrt x^{2}$$ $$x=±2$$. Therefore, you now have points $(0,-4), (2,0)\: and \:(-2,0)$.
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