Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 3 - Linear and Quadratic Functions - 3.3 Quadratic Functions and Their Properties - 3.3 Assess Your Understanding - Page 146: 56


The graph has a maximum value of $18$.

Work Step by Step

RECALL: (1) The graph of the quadratic function $f(x)=ax^2=bx+c$ opens: (i) upward when $a \gt0$ and has its vertex as its minimum; or (ii) downward when $a\lt0$ and has its vertex as its maximum. (2) The vertex of the quadratic function $f(x)=ax^2=bx+c$ is at $\left(-\frac{b}{2a}, f(-\frac{b}{2a})\right)$ Let's compare $f(x)=-2x^2+12x$ to $f(x)=ax^2+bx+c$. We can see that $a=-2$, $b=12$, $c=0$. $a\gt0$, hence the graph opens down, hence it's vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{12}{2\cdot (-2)}=3.$ Thus, the maximum value is $f(3)=-2(3)^2+12(3)=18.$
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.