College Algebra (10th Edition)

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

Chapter 3 - Section 3.5 - Graphing Techniques: Transformations - 3.5 Assess Your Underdstanding - Page 257: 7


Option (B)

Work Step by Step

The graph involves a parabola, so its parent function is $y=x^2$. The parabola opens downward, so the function involves a reflection of the parent function about the x-axis. Thus, a tentative equation would be $y=-x^2$. The vertex of the parent function is at $(0, 0)$. The vertex of the given function is at $(0, 2)$, which involves a 2-unit vertical shift of the parent function. Thus, the equation of the given function is: $y=-x^2+2$ Therefore, the answer is Option (B).
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