Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - Guided Practice for Examples 6 and 7 - Page 287: 13


The vertex form of the function is $y=(x-4)^{2}+1.$ The vertex is $(4,1)$.

Work Step by Step

$ y=x^{2}-8x+17\qquad$ ...prepare to complete the square. $ y+(?)=x^{2}-8x+(?)+17\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-8}{2})^{2}=(-4)^{2}=16\qquad$ ...add $16$ to each side of the expression $ y+(16)=x^{2}-8x+(16)+17\qquad$ ... write $x^{2}-8x+16$ as a binomial squared. $ y+16=(x-4)^{2}+17\qquad$ ...add $-16$ to each side of the expression $ y+16-16=(x-4)^{2}+17-16\qquad$ ...simplify. $y=(x-4)^{2}+1$ The vertex form of a quadratic function is $y=a(x-h)^{2}+k$ where $(h,k)$ is the vertex of the function's graph. Here, $h=4,\ k=1$, so the vertex is $(4,1)$
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.