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

Jun 24, 2018

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:

$x = \frac{1}{4 p} {\left(y - k\right)}^{2} + h$

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

$x = \frac{1}{4} {\left(y - 2\right)}^{2} - 1$