Question

What is the vertex form of `y= x^2 -x - 11`?

Answer 1

Vertex form is `(x-1)^2=y+45/4`.
The vertex or this parabola is `V(1, -45/4)`

Explanation:

The equation `(x-alpha)^2=4a(y-beta)` represents the parabola with

vertex at `V( alpha, beta)`, axis VS along `x = alpha`, focus at

`S(alpha, beta+a)` and directrix as `y=beta-a`

Here, the given equation can be standardized as

`(x-1)^2=y+45/4`. giving `a = 1'4, alpha = 1 and beta =-45/4`.

Vertex is `V(1, -45/4)`

Axis is x=1.

Focus is S(1, -11).

Directrix is `y=-49/4`