College Algebra (10th Edition)

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

Chapter 4 - Section 4.3 - Quadratic Functions and Their Properties - 4.3 Assess Your Understanding - Page 299: 27

Answer

See image
1564396951

Work Step by Step

Write $f$ in the form $f(x)=a(x-h)^{2}+k$: $\begin{aligned}f(x)&=2x^{2}-4x+1\\&=2\left(x^{2}-2x\right)+1\\&=2\left(x^{2}-2x+1\right)+1-2\\&=2(x-1)^{2}-1\end{aligned}$ Let $f_{1}(x)=x^{2}$. Then, $f(x)=2f_{1}(x-1)-1$. The graph is obtained from $f_{1}(x)$ by - vertical stretching by factor $2,$ - shifting to the right by 1 unit, - and then down by 1 unit Point by point, $\left[\begin{array}{lllll} (x,y) & \rightarrow & (x,2y) & \rightarrow & (x+1,2y-1)\\ & & & & \\ (0,0) & \rightarrow & (0,0) & \rightarrow & (1,-1)\\ (-1,1) & \rightarrow & (-1,2) & \rightarrow & (0,1)\\ (1,1) & \rightarrow & (1,2) & \rightarrow & (2,1)\\ (-2,4) & \rightarrow & (-2,8) & \rightarrow & (-1,7)\\ (2,4) & \rightarrow & (2,8) & \rightarrow & (3,7) \end{array}\right]$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.