Question

How do you find the axis of symmetry and vertex point of the function: `y = x^2 − 1`?

Answer 1

Rewrite in explicit vertex form and recognize it as a parabola in standard position.
Vertex:`(0,-1)color(white)("XXXX")`Axis of symmetry: `x=0`

Explanation:

Vertex form of a parabola in standard position:
`color(white)("XXXX")y=m(x-color(red)(a))^2+color(blue)(b)`
`color(white)("XXXXXXXX")`with vertex at `(a,b)` and opening upward if `m>0`

`y=x^2-1`
can be written in explicit vertex form as
`color(white)("XXXX")y=1(x-color(red)(0))^2+color(blue)((-1))`
`color(white)("XXXXXXXX")`with vertex at `(color(red)(0),color(blue)(-1))`

In standard position the axis of symmetry is a vertical line through the vertex; i.e. `x=color(red)(0)`