Question

How do you write an equation for the parabola with vertex (-1,2) and directrix x=-2?

Answer 1

We need to know the value of `p` in order to write the equation.

Explanation:

Since the vertex is the same distance from both the focus and the directrix, we don't need to know the focus. The vertex is at the x-value of `-1` and the directrix is 1 unit away at `x=-2`, so `p=1`.

Before we go any further, we should know that the directrix is always outside of the parabola. Since it's a vertical line and is to the left of the parabola, the graph opens to the right. Here's the standard form for a right-facing parabola:

`x=1/(4p)(y-k)^2+h`

We can use this to find our scale factor. We know that `p=1`, so the scale factor is `1/4`. We can also plug in the values for our vertex to get our equation:

`x=1/4(y-2)^2-1`