The altitude of a kicked football can be described with the function h(?) = −0.01?2 + 1.18? + 2, where x, in feet, is the horizontal distance from the point of impact with the punter’s foot. a. Find the vertex of the parabola. b. If the opposite team does not catch the ball, how far away from the kicker does the ball hit the ground? c. What is the maximum height of the ball? d. How far downfield has the ball traveled when it reaches a height of 6 feet for the second time?

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A: Please refer the attached image for complete solution.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.