College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Review - Exercises: 76

Answer

maximum: $(-\frac{1}{2},\frac{5}{4})$ no minimas

Work Step by Step

We are given: $f(x)=1-x-x^{2}$ We factor by completing the square: $1-x-x^{2}$ $-x^2-x+1$ $-(x^{2}+x)+1$ $-(x^{2}+x+\displaystyle \frac{1}{4})+1+\frac{1}{4}$ $-(x+\frac{1}{2})^{2}+\frac{5}{4}$ We see that this is a transformed parabola: $x^2$ reflected around the x-axis, moved left $\frac{1}{2}$ units and up $\frac{5}{4}$ units. Thus the maximum would occur at $(-\frac{1}{2},\frac{5}{4})$.
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