Chapter 1 - Precalculus Review - 1.2 Linear and Quadratic Functions - Exercises - Page 19: 39

$ y=-7$ is the minimum, when $ x=-3$

Given $$ y= x^{2}+6 x+2 $$ So, we have \begin{aligned} y&= x^{2}+6 x+2 \\ &= x^{2}+6 x+2+7-7 \\ &= x^{2}+6 x+9-7 \\ &=( x^{2}+6 x+9)-7 \\ &=( x+3)(x+3)-7 \\ &=( x+3)^2-7 \\ \end{aligned} The lowest value for the squared term is $0$. So, we see that $ y=-7$ is the minimum, when $ x=-3$.