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

1 Answer
Jun 24, 2018

Answer:

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#