College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Summary, Review, and Test - Review Exercises - Page 435: 6

Answer

a. The minimum point is $(-3,685).$ b. Domain: $(-\infty,\infty)$ Range: $(685,\infty)$

Work Step by Step

See p.337. Consider the quadratic function $f(x)=ax^{2}+bx+c$. 1. If $a > 0$, then $f$ has a minimum that occurs at $x=-\displaystyle \frac{b}{2a}$ . This minimum value is $f$($-\displaystyle \frac{b}{2a}$). 2. If $a < 0$, then $f$ has a maximum that occurs at $x=-\displaystyle \frac{b}{2a}$. This maximum value is $f$($-\displaystyle \frac{b}{2a}$) -------------------------- a. $a = 2 > 0$, so $f$ has a minimum that occurs at $x=-\displaystyle \frac{b}{2a}$ $-\displaystyle \frac{b}{2a}=-\frac{12}{2(2)}=-3,\quad $ $f(3)=2(-3)^{2}+12(-3)+703=18-36+703=685$ The minimum point is $(-3,685).$ b. f(x) is defined all real numbers. f(x) has minimum value $685$ no maximum. Domain: $(-\infty,\infty)$ Range: $(685,\infty)$ a. The minimum point is $(-3,685).$ b. Domain: $(-\infty,\infty)$ Range: $(685,\infty)$
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