In order to successfully perform a trick, a flying trapeze artist must swing along a parabolic path that is equidistant from the floor and the pivot point where the trapeze rope is attached. the rope is attached to the ceiling 8 feet out and 16 feet above her starting point and the floor is 8 feet below her starting point. find the vertex of this parabola using the focus of (8,16) and directrix at y = -8.

Given that the directrix of the parabola is at y = -8 and the focus is at point (8, 16), this means that the parabola opens upwards and the x part of the equation of the parabola is squared. The x-value of the vertex of a parabola is the same as the x-value of the focus while the y-value of the vertex is half the sum of y-values of the focus and the directrix. Therefore, the vertex of the given parabola is (8, (16 - 8)/2) = (8, 8/2) = (8, 4).