Question

What is the the vertex of `y = (x-3)(x+5) -x+12`?

Answer 1

`(-1/2, -13/4)`

Explanation:

The equation `x-alpha)^2` = `4 a (y-beta)` represents the parabola with vertex at `(alpha, beta)`
The focus is at `(alpha, beta+a)`.
Our equation is equivalent to `(x+1/2)^2` = `4(1/4)(y+13/4)`
Vertex is `(-1/2, -13/4)`
Focus is `(-1/2, -3)` .