Answer:
The parabola has a vertex at (5, -4), has a p-value of 3, and it opens to the right.
Explanation:
For a parabola given a focus and a directrix, the vertex is the midpoint between the focus and the directrix. In this case, the focus is at (8, -4), and the directrix is the vertical line x = 2. Therefore, the vertex is at the x-coordinate that lies between the focus and the directrix, which is (5, -4).
The p-value represents the distance between the vertex and either the focus or the directrix. Since the parabola opens to the right, the p-value is the distance between the vertex and the focus, which is 3.
Finally, since the directrix is a vertical line (x = 2), and the parabola opens to the right, we can conclude that the parabola opens to the right.