Answer:
[tex]y=\frac{1}{12}(x+5)^2+2[/tex]
Step-by-step explanation:
We start with the standard form of a parabola which is
[tex](x-h)^2=4p(y-k)[/tex]
We know h and k from the vertex, we just need to solve for p and then simplify the equation. P, by definition, is the distance between the directrix and the vertex. That is 3 units. So p = 3. Fitting that into our equation along with h and k gives us:
[tex](x+5)^2=4(3)(y-2)[/tex]
Divide both sides by 12, then add the 2 to both sides and we have our parabola!
