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 - 4.7 Exercises - Quiz for Lessons 4.5-4.7 - Page 291: 17


The vertex form of the function is $y=(x-(-\displaystyle \frac{1}{2}))^{2}+\frac{3}{4}.$ The vertex is $(-\displaystyle \frac{1}{2},\frac{3}{4})$.

Work Step by Step

$ y=x^{2}+x+1\qquad$ ...write in form of $x^{2}+bx=c$ (add $-1$ to each side). $ y-1=x^{2}+x\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{1}{2})^{2}=\frac{1}{4}\qquad$ ...complete the square by adding $\displaystyle \frac{1}{4}$ to each side of the expression $ y-1+\displaystyle \frac{1}{4}=x^{2}+x+\frac{1}{4}\qquad$ ... write $x^{2}-x+\displaystyle \frac{1}{4}$ as a binomial squared. $ y-\displaystyle \frac{3}{4}=(x+\frac{1}{2})^{2}\qquad$ ...add $\displaystyle \frac{3}{4}$ to each side of the expression $ y=(x+\displaystyle \frac{1}{2})^{2}+\frac{3}{4}\qquad$ ...write in vertex form $y=a(x-h)^{2}+k$. $y=(x-(-\displaystyle \frac{1}{2}))^{2}+\frac{3}{4}$ 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, $h=-\displaystyle \frac{1}{2},\ k=\displaystyle \frac{3}{4}$, so the vertex is $(-\displaystyle \frac{1}{2},\frac{3}{4})$
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.