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 Graph Quadratic Functions in Standard Form - 4.1 Exercises - Problem Solving - Page 242: 56


They should decrease the price by $20$.

Work Step by Step

$R(x)=(320-20x)(70+5x)=-100x^2+200x+22400$ Let's compare $R(x)=-100x^2+200x+22400$ to $f(x)=ax^2+bx+c$. We can see that a=-100, b=200, c=22400. $a\lt0$, hence the graph opens down, and its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{200}{2\cdot(-100)}=1.$ Hence the maximum value is $f(1)=-100(1)^2+200(1)+22400=22500.$ Thus they should decrease the price by $20$.
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