Question

How do you write the equation of the parabola in vertex form given Vertex: ( -1, 2), Focus (-1, 0)?

Answer 1

The vertex form of a parabola where the vertex and the focus are separated by a vertical distance is:

`y = 1/(4f)(x - h)^2+k" [1]"`

Where `(h,k)` is the vertex and `f` is the signed distance from the vertex to the focus.

Substitute the given vertex, `(-1,2)`, into equation [1]:

`y = 1/(4f)(x - (-1))^2 + 2" [2]"`

Compute the value of `f` by subtracting the y coordinate of the vertex from the y coordinate of the focus:

`f = 0-2`

`f = -2`

Substitute the value for `f` into equation [2]:

`y = 1/(4(-2))(x - (-1))^2 + 2`

`y = -1/8(x - (-1))^2 + 2" [3]"`

Equation [3] is the answer.