Need help to know how to do this problem!!

Question

A parabola has a focus located at      and a directrix of    .

What are the coordinates for the vertex?     

The equation for this parabola in vertex form is as follows:

         

Answer 1

In your first post of this type, I provided this general procedure (and I also solved the particular problem). If you have questions on how to apply this to each different problem, you can post a comment.

The general form of a parabola:

Opening left or right: y² = 4ax (Opening left: -4ax)

Opening up or down: x² = 4ay (Opening down: -4ay)

To remember which is which: If it opens up or down, then there are 2 x values for every y value--similar logic for right and left.

If the vertex is not at the origin, then we apply offsets: If the origin is at (j, k), then replace x with x - k, and replace y with y = k

a is the distance from the vertex to either the focus or directrix. (2a is the distance from focus to directrix)

So...the steps:

1. Put the equation into the form described above
2. Find a and use that to determine the relative location of focus, vertex, and directrix
3. PLOT the function to verify your results