# What is the axis of symmetry and vertex for the graph y=2(x+3)^2+6?

Aug 11, 2017

Vertex is at $\left(- 3 , 6\right)$. Axis of symmetry is $x = - 3$

#### Explanation:

$y = 2 {\left(x + 3\right)}^{2} + 6$

Comparing with standard vertex form of equation

y = a(x-h)^2 +k ; (h,k) being vertex , we find here

$h = - 3 . k = 6$ So Vertex is at $\left(- 3 , 6\right)$.

Axis of symmetry is $x = h \mathmr{and} x = - 3$

graph{2(x+3)^2+6 [-40, 40, -20, 20]}

Aug 11, 2017

$x = - 3 , \left(- 3 , 6\right)$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where ( h , k ) are the coordinates of the vertex and a is a constant.

$y = 2 {\left(x + 3\right)}^{2} + 6 \text{ is in this form}$

$\text{with "h=-3" and } k = 6$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 3 , 6\right)$

$\text{the axis of symmetry passes through the vertex, is vertical}$

$\text{with equation } x = - 3$