# What is the axis of symmetry and vertex for the graph y = -x^2 – 2x – 13?

May 4, 2017

$x = - 1 , \left(- 1 , - 12\right)$

#### Explanation:

$\text{for the standard quadratic function } y = a {x}^{2} + b x + c$

"equation of axis of symmetry is " x=-b/(2a)=x_(color(red)"vertex")

$\text{for } y = - {x}^{2} - 2 x - 13$

$\text{then " a=-1,b=-2" and } c = - 13$

$\text{equation of axis of symmetry } = - \frac{- 2}{- 2} = - 1$

$\Rightarrow \text{ axis of symmetry } x = - 1$

$\text{substitute this value into function and evaluate for y}$

${y}_{\textcolor{red}{\text{vertex}}} = - {\left(- 1\right)}^{2} - 2 \left(- 1\right) - 13 = - 12$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 1 , - 12\right)$