Question

Write an equation of a parabolawith a vertex (-5,2) and a directrix y = -1.

Answer 1

`y=(1)/(12)(x+5)^2+2`

Explanation:

We start with the standard form of a parabola which is

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

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:

`(x+5)^2=4(3)(y-2)`

Divide both sides by 12, then add the 2 to both sides and we have our parabola!