# How do you find the axis of symmetry for this parabola: y= -5x^2- 10x -15?

Nov 3, 2016

The axis of symmetry is $x = - 1$

#### Explanation:

We have to change the equation to the vertex form
$y = - 5 \left({x}^{2} + 2 x\right) - 15$
$y = - 5 \left({x}^{2} + 2 x + 1\right) - 15 + 5$
$y = - 5 {\left(x + 1\right)}^{2} - 10$
From the equation of the parabola, we deduce the axis of symmetry
As $x = - 1$
graph{-5x^2-10x-15 [-24.1, 21.52, -22.07, 0.75]}

Nov 3, 2016

$x = - 1$ is the axis of symmetry.

#### Explanation:

$y = - 5 {x}^{2} - 10 x - 15 \text{ } \leftarrow a {x}^{2} + b x + c$

The axis of symmetry can be found directly from the formula $x = \frac{- b}{2 a}$

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

$x = \frac{10}{-} 10 = - 1$

Note that this is a vertical line with the x-intercept at $\left(- 1 , 0\right)$