College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 4 - Section 4.3 - Quadratic Functions and Their Properties - 4.3 Assess Your Understanding - Page 301: 88


a) $20000$ b)$2000$

Work Step by Step

Let's compare $f(x)=5x^2-200x+4000$ to $f(x)=ax^2+bx+c$. We can see that a=5, b=-200, c=4000. a>0, hence the graph opens up, hence its vertex is a minimum. The minimum value is at $x=-\frac{b}{2a}=-\frac{-200}{2\cdot 5}=20.$ Hence the minimum value is $f(20)=5(20)^2-200(20)+4000=2000.$ Thus: a) $20000$ b)$2000$
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