# What is the axis of symmetry and vertex for the graph y=x^2+8x+12?

May 10, 2018

The axis of symmetry is $x = - 4$, the vertex is $\left(4 , - 4\right)$

#### Explanation:

We can find the axis of symmetry in the form of a line, $x$

To find the value of line $x$, we use this equation:
$x = \frac{- b}{2 a}$.

In our given graph, $a = 1$, and $b = 8$

After inserting values:

$x = \frac{- 8}{2 \cdot 1} = \frac{- 8}{2} = - 4$

The equation for our axis of symmetry is $x = - 4$

To find the vertex, we must convert our parabola's equation to vertex form: $y = a {\left(x - h\right)}^{2} + k$. We can do this by completing the square.

$y = {x}^{2} + 8 x + 12$

$y - 12 = {x}^{2} + 8 x$

$y - 12 + 16 = {x}^{2} + 8 x + 16$

$y + 4 = {\left(x + 4\right)}^{2}$

$y = {\left(x + 4\right)}^{2} - 4$

$h = - 4 , k = - 4$

Our vertex is h,k, and thus, (-4,-4).