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 213: 62a


Horizontal shift, vertical shrink, reflection, horizontal shift (see graph)

Work Step by Step

We are given the function: $N(x)=-0.023(x-33.12)^2+131$, $0\leq t\leq 14$ Describe the transformation of the parent function $f(x)=x^2$. Horizontally shift $f(x)$ 33.12 units to the right to get $a(x)=(x-33.12)^2$. Vertically shrink $a(x)$ by a factor of 0.023 to get $b(x)=0.023(x-33.12)^2$. Reflect $b(x)$ across the $x$-axis to get $c(x)=-0.023(x-33.12)^2$. Vertically shift $c(x)$ 131 units upward to get $N(x)=-0.023(x-33.12)^2+131$. Graph $N(x)$.
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