#2**+4 **

Ah, here it is!

The vertex has to be right in between them, so the vertex is \((0, 2)\). Now, we use the equation \((x-h)^2=4p(y-k)\). \(p = -2\) , because that is the directed distance between the vertex and focus. We get than \(x^2 = -8(y-2)\), so

\(\boxed{y = -\frac{1}{8}x^2+2}\) is the desired equation.

tertre Apr 25, 2018