Explain the steps you would use to determine the path of the ball in terms of a transformation of the graph of y = x2.

Answer:

To determine the path of the ball, first complete the square to rewrite the quadratic equation in vertex form, y = a(x - h)^2 + k. For the equation y = -16(x - 1)^2 + 19, the transformations include a reflection across the x-axis and a vertical stretch that makes the graph narrower because a = -16. Additionally, identify the translations: the graph is shifted 1 unit to the right (h = 1) and 19 units up (k = 19).