Question

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

Answer 1

The axis of symmetry is `x=-1`

Explanation:

We have to change the equation to the vertex form
`y=-5(x^2+2x)-15`
`y=-5(x^2+2x+1)-15+5`
`y=-5(x+1)^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]}

Answer 2

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

Explanation:

`y = -5x^2 -10x -15 " "larr ax^2 +bx +c`

The axis of symmetry can be found directly from the formula `x = (-b)/(2a)`

`x = (-(-10))/(2(-5))`

`x = 10/-10 = -1`

Note that this is a vertical line with the x-intercept at `(-1, 0)`