Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.5 - Transformations of Functions - 2.5 Exercises - Page 211: 47a



Work Step by Step

Since the shape of the graph is a $f(x) = x^2$ we will start with that function: $f(x)=x^2$ The first thing to notice is the graph is reflected across the x-axis. The reflection across the x-axis means multiply the right side by -1 $f(x)=-x^2$ The second thing to notice is the graph is stretched vertically by a factor of 3 because $f(x)=-x^2$ passes through (1,-1) but the graph goes through (1,-3). To apply vertical stretches, multiply the right side by the factor. $f(x)=-3x^2$
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