Answer
$ y=4$
Work Step by Step
Given $$ y=x^{2}+2 x+5$$
So, we have
\begin{aligned} y&=x^{2}+2 x+5\\
&=x^{2}+2 x+1 -1+5\\
&=(x^{2}+2 x+1) +4\\
&=(x+1)^{2}+4\\
\end{aligned}
So, we see that $ y=4$ is the minimum, when $ x=-1$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 1 - Precalculus Review - 1.2 Linear and Quadratic Functions - Exercises - Page 19: 36
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