Janiah plays second base (position 4 as shown in the picture). She can throw a softball in a perfect parabolic arc to throw out a runner trying to steal home plate (position 2), which also is 70 feet.  Assume that Janiah let's go of the ball 5 feet above the ground and the catcher (position 2) catches it 5 feet above the ground. The ball reaches a maximum height of 20 feet above the ground halfway to the catcher. What is an equation of the path of the softball? Explain the reasoning

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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.