Explain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.

Step-by-step explanation:

You didn't write the coordinates of either the focus or the directrix, but you really don't need them to list the "rules" for where the vertex falls in a coordinate plane. The rules for this are that:

1. the vertex is located exactly halfway between the focus and the directrix

2. the vertex is on the same axis as the focus

3. the coordinates of the vertex are (h, k)

There are 4 different cases for the coordinates of a focal point and a directrix.

1. If the parabola opens upwards, the vertex is at (h, k), the focus is at (h, k + p) and the directrix is at y = k - p

2. If the parabola opens downward, the vertex is at (h, k), the focus is at (h, k - p) and the directrix is at y = k + p

3. If the parabola opens to the left, the vertex is at (h, k), the focus is at (h - p, k), and the directrix is at x = h + p

4. If the parabola opens to the right, the vertex is at (h, k), the focus is at (h + p, k), and the directrix is at x = h - p

where p is the distance between the vertex and the focus OR the vertex and the directrix (they are the same distance since the vertex is directly in between them).