# How do you find the axis of symmetry and the vertex for y = -x^2 -10x?

Mar 24, 2017

Axis of symmetry: $x = - 5$

The vertex is at $\left(- 10 , 25\right)$

#### Explanation:

There is a formula to find the axis of symmetry of a parabola.
The standard form of a parabola is $y = a {x}^{2} + b x + c$

Axis of symmetry: $x = \frac{- b}{2 a}$

We have $y = - {x}^{2} - 10 x$

$a = - 1 \mathmr{and} b = - 10$

$x = \frac{- \left(- 10\right)}{2 \left(- 1\right)} = \frac{10}{-} 2 = - 5$

$x = - 5$ is the line of symmetry.

The vertex lies on the line of symmetry, so as soon as you have the $x$-value, you can find the $y$-value.

$y = - {\left(- 5\right)}^{2} - 10 \left(- 5\right)$

$y = - 25 + 50$

$y = 25$

The vertex is at $\left(- 10 , 25\right)$