Question

How do you find the axis of symmetry and vertex point of the function: `y=x^2+12x-9`?

Answer 1

Axis of Symmetry: `x=-6`
Vertex: `(-6,-45)`

Explanation:

The first thing you must do, is convert this equation to vertex form `y=a(x-h)^2+k`. Finding the axis of symmetry and the vertex will become easy after that.

Converting to Vertex Form (`y=a(x-h)^2+k`)
`y=x^2+12x-9`
`y+9=x^2+12x`
`y+9+36=x^2+12x+36`
`y+45=(x+6)^2`
`color(red)(y=(x+6)^2-45)`

Axis of Symmetry
The axis of symmetry is `x=h`. Just by looking at the equation in vertex form, you will see that `h=-6`.

Therefore, the axis of symmetry is:

`x=h`
`color(blue)(x=-6)`

Vertex
The vertex is `(h,k)`. Again, just look at the equation and you will see that `h=-6` and `k=-45`.

Therefore, the vertex is:

`(h,k)`
`color(magenta)((-6,-45)`