Question

What is the axis of symmetry and vertex for the graph `p(x)=(x+5)^2-3`?

Answer 1

The vertex is at `(-5,-3)`, and the axis of symmetry is at `x=-5`.

Explanation:

This quadratic function is written in "vertex form", or `y=a(x-h)^2+k`, where `(h,k)` is the vertex. This makes it really easy to see that, since `(x+5) = (x-h)`, `h=-5`. Remember to change the sign of `h` when you see a quadratic in this form.
Since the `x^2` term is positive, this parabola opens upward.

The axis of symmetry is just an imaginary line that goes through the vertex of a parabola where you would fold if you folded the parabola in half, with one side on top of the other.

Since that would be a vertical line through `(-5,-3)`, the axis of symmetry is `x=-5`.