Question

How do you turn a standard form to vertex form `y=x^2-1`?

Answer 1

For the given equation the vertex form is
`color(white)("XXX")y=(x-0)^2+(-1)`

Explanation:

The general vertex form is
`color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)`
for a parabola with vertex at `(color(red)(a),color(blue)(b))`

The given equation: `y=x^2-1`
can be converted into an explicit vertex form as
`color(white)("XXX")y=color(green)(1)(x-color(red)(0))^2+color(blue)(""(-1))`
with vertex at `(color(red)(0),color(blue)(-1))`