Software was used to analyze a video of the path of a thrown ball. The position of the ball was measured three times. The coordinates obtained are shown in the table (x and y are measured in feet)
Horizontal Distance, x
0 15 30
Height, y
50 0.8 12.3
(a) Write a system of equations to find the equation of the parabola y-ax²+
that passes through the three points (Enter your answers as a comma-separated but of equations).
(b) Solve the system using matrices. (Round all numerical values to four decimal places)
(C) Use a graphing utility to graph the approximate the maximum height of the ball and the point at which the ball struck the ground. (Round your answers to the nearest whole number)
maximum height
point at which the ball strikes the ground
(d) Analytically find the maximum height of the ball and the point at which the ball struck the ground. (Round your answers to three decimal places.)
maximum height
point at which the ball strikes the ground
(e) Compare your results from parts (d) and (e)
O The results are similar
The results are comiderably different
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