Question

A ball is thrown straight up from a height of 3 ft with a speed of 32 ft/s. Its height above the ground after x seconds is given by the quadratic function y = -16x2 + 32x + 3. 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 1

It would be determined by understanding the different paths it can take- the one we have is a reflection.

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Answer 2

Complete the square to get the equation in vertex form with
a = -16, h = 1, and k = 19. The path is a reflection over the x-axis and narrower. It is also translated right 1 unit and up 19 units.