Question

How do you find the vertex of a parabola `y=x^2+2x-1`?

Answer 1

The vertex of a parabola occurs when its derivative is equal to `0`

`y = x^2+2x-1`

`y' = 2x +2 = 0` for the vertex
that is
`x=-1` at the vertex

Substituting `x=-1` back into the original equation gives
`y = (-1)^2+2(-1)-1`
`=1 -2 -1 = -3`

So the vertex of the parabola occurs at `(-1,-3)`