# What is the axis of symmetry and vertex for the graph y = 2x^2 + 24x + 62?

Aug 24, 2017

The axis of symmetry is $- 6$.

The vertex is $\left(- 6 , - 10\right)$

#### Explanation:

Given:

$y = 2 {x}^{2} + 24 x + 62$ is a quadratic equation in standard form:

$y = a {x}^{2} + b x + c$,

where:

$a = 2$, $b = 24$, and $c = 62$.

The formula for finding the axis of symmetry is:

$x = \frac{- b}{2 a}$

Plug in the values.

$x = - \frac{24}{2 \cdot 2}$

Simplify.

$x = - \frac{24}{4}$

$x = - 6$

The axis of symmetry is $- 6$. It is also the $x$ value for the vertex.

To determine $y$, substitute $- 6$ for $x$ and solve for $y$.

$y = 2 {\left(- 6\right)}^{2} + 24 \left(- 6\right) + 62$

Simplify.

$y = 2 \left(36\right) + \left(- 144\right) + 62$

$y = 72 - 144 + 62$

$y = - 10$

The vertex is $\left(- 6 , - 10\right)$.