Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 254: 67

Answer

$m,n$ $(m+n)/2$

Work Step by Step

Clearly the x-intercepts are given by the x values when $f(x)=0$ which means $x=m,n$. Based on the symmetry of the parabola curve, the vertex happens at the middle points of the two x-intercepts, which give $x_v=\frac{m+n}{2}$. We can confirm this by expanding the function $f(x)=(x-m)(x-n)=x^2-mx-nx+mn=x^2-(m+n)x+mn$, and this expression indicates that the vertex happens at $x=(m+n)/2$
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.