Question

What is the axis of symmetry and vertex for the graph `y = -2x^2 - 12x - 7`?

Answer 1

The axis of symmetry is `-3` and the vertex is `(-3,11)`.

Explanation:

`y=-2x^2-12x-7` is a quadratic equation in standard form: `ax^2+bx+c`, where `a=-2`, `b=-12`, and `c=-7`.

The vertex form is: `a(x-h)^2+k`, where the axis of symmetry (x-axis) is `h`, and the vertex is `(h,k)`.

To determine the axis of symmetry and vertex from the standard form: `h=(-b)/(2a),` and `k=f(h)`, where the value for `h` is substituted for `x` in the standard equation.

Axis of Symmetry

`h=(-(-12))/(2(-2))`

`h=12/(-4)=-3`

Vertex

`k=f(-3)`

Substitute `k` for `y`.

`k=-2(-3)^2-12(-3)-7`

`k=-18+36-7`

`k=11`

The axis of symmetry is `-3` and the vertex is `(-3,11)`.

graph{y=-2x^2-12x-7 [-17, 15.03, -2.46, 13.56]}