Question

How do you write the equation of the parabola in vertex form given vertex (0,0) and the directrix y=-16?

Answer 1

`y=1/64 x^2`

Explanation:

Given -

Vertex `(0, 0)`
Directrix `(y=-16)`
Focus `(0,16)`

The Parabola is opening up, as its directrix is `y=-16`

The formula for the parabola in the vertex form is -

`(x-h)^2=4.a.(y-k)^2`

Where -

`h = 0` x-coordinate of the vertex
`k=0` y-coordinate of the vertex
`a=16` distance between vertex and focus

`x-0)^2=4xx16(y-0)`
`x^2=64y`
`y=1/64 x^2`