Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.4 Properties of Quadratic Functions - 2.4 Assess Your Understanding - Page 158: 51



Work Step by Step

1) The graph of the quadratic function $f(x) = ax^2+bx+c$ is a parabola that opens: (a) Upward when $a \gt 0$ and its vertex has a minimum value. (b) Downward when $a \lt 0$ and its vertex has a maximum value. On comparing $f(x)=2x^2+12x$ with $f(x) = ax^2+bx+c$, we get: $a=2, b=12,c=0; a \gt 0$. We can see that the given function shows a graph of a parabola that opens upward. 2) The coordinates of the vertex of a quadratic function $f(x) = ax^2+bx+c$ are given by: $\displaystyle(\frac{-b}{2a}, f(-\frac{2}{a}))$ Thus, the minimum value at $x$ can be expressed as: $x=\displaystyle \frac{-b}{2a}=\frac{-(12)}{2(2)}=-3$ Therefore, the minimum 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.