Question

Select the equation that represents a problem that opens down from a vertex of (32,26) and has a focus located 20 units away from the vertex

Answer 1

Explanation:

If the parabola opens downward, and we have a p value (which is the distance from the vertex to the focus), the form of the equation we need is:

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

If the vertex is (32, 26), then h = 32 and k = 26. If the focus is located 20 units from the vertex, then p = 20. Filling in:

`-(x-32)^2=4(20)(y-26)` and

`-(x-32)^2=80(y-26)` and

`-(1)/(80)(x-32)^2=y-26` so the equation is

`-(1)/(80)(x-32)^2+26=y`

You didn't give choices so I'm not sure what form you need this in. This is vertex (or work) form.