Question

What is the vertex of the parabola given by `y = x^2-2px+q` ?

Answer 1

`(-p, q-p^2)`

Explanation:

`(x+p)^2 = x^2+2px+p^2`

So:

`y = x^2+2px+q = (x+p)^2 + (q-p^2)`

`(x+p)^2 >= 0` and is zero when `x = -p`

If `x = -p` then `y = 0+(q-p^2) = q-p^2`