Question

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

Answer 1

Axis of symmetry is `x=0` i.e. `y`-axis and vertex is `(0,-7)`.

Explanation:

A general equation of a parabola is `y=a(x-h)^2+k`, where `(h,k)` is the vertex and `x-h=0` is the axis of symmetry.

Observe that we can write the given equation `y=x^2-7` as

`y=1xx(x-0)^2-7`

and hence while axis of symmetry is `x=0` i.e. `y`-axis and vertex is `(0,-7)`.

graph{(y-x^2+7)(x^2+(y+7)^2-0.02)=0 [-20, 20, -10, 10]}