Algebra 2 (1st Edition)

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

Chapter 4 Quadratic Functions and Factoring - 4.1 Quadratic Functions in Standard Form - 4.1 Exercises - Skill Practice - Page 241: 38


See below.

Work Step by Step

Let's compare $f(x)=-0.25x^2-7x+2$ to $f(x)=ax^2+bx+c$. We can see that a=-0.25, b=-7, c=2. $a\lt0$, hence the graph opens down, and its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{-7}{2\cdot(-0.25)}=-14.$ Hence the maximum value is $f(14)=-0.25(14)^2-7(-14)+2=51.$
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