Question

How do I find the directrix of the parabola whose equation is `y=x^2/32`?

Answer 1

You have a parabola with vertex at `(0, 0)` that is opening upward.

That means your directrix is horizontal.

To get the directrix, transfer `x^2`'s coefficient to the other side.
Equate the resulting coefficient of `y` to `4d`, where `d` is the distance from the vertex to the directrix

`y = x^2/32`
`=> 32y = x^2`

`4d = 32`
`=> d = 8`

Since the parabola is opening upward, the directrix is below the vertex.

`y = h - d`

`y = 0 - 8`

`y = -8`