Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 252: 25


a. $f(x)=(x+1)^{2}-2$ b. see image below c. Minimum value $f(-1)= -2$

Work Step by Step

a. Complete the square: $(x^{2}+2x+1-1) -1=(x+1)^{2}-1-1$ $f(x)=(x+1)^{2}-2$ b. To sketch, begin with the parent function $f_{1}(x)=x^{2},$ (blue, dashed line in the image) and, since $f(x)=f_{1}(x+1)-2,$ shift the graph to the left by 1 unit, and down 2 units (solid red line, see image) c. The graph of $f(x)=a(x-h)^{2}+k$ is a parabola, and, if $a > 0$, then the quadratic function $f$ opens upward and has the minimum value $k$ at $x=h=-\displaystyle \frac{b}{2a}$. Minimum value $f(-1)=-2$
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