# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=x^2+6x+2?

$x = - 3 \text{ }$ is the axis of symmetry

#### Explanation:

the vertex of the parabola is at $\left(h , k\right) = \left(- 3 , - 7\right)$
by the formula

$h = - \frac{b}{2 a}$ and $k = c - {b}^{2} / \left(4 a\right)$

from the given $y = {x}^{2} + 6 x + 2$
$a = 1$, $b = 6$, and $c = 2$

$h = - \frac{b}{2 a} = - \frac{6}{2 \cdot 1} = - 3$

$k = c - {b}^{2} / \left(4 a\right) = 2 - {6}^{2} / \left(4 \cdot 1\right) = 2 - \frac{36}{4} = 2 - 9 = - 7$

The minimum point is the vertex $\left(- 3 , - 7\right)$
graph{y=x^2+6x+2 [-13.58, 6.42, -8.6, 1.4]}

and clearly $x = - 3$ a vertical line which passes thru $\left(- 3 , - 7\right)$ is the line of symmetry.

God bless....I hope the explanation is useful.