Write the equation of the parabola below : vertex (5,-3); directrix x=2

Answer 1

directrix is to the left of the vertex---this means that the parabola opens to the right. We can use the form:

y² = 4ax, where a is the distance from the vertex to either the focus or directrix. From the information given, a = 3.

The vertex is at (5,-3), so we need a y offset of +3, and an x offset of -5. Putting it all together:

(y + 3)² = 12(x - 5)

CHECK by graphing the function