Water flowing from a horizontal pipe 48 feet above the ground has the shape of a parabola whose vertex  (0, 48)  is at the end of the pipe (see figure). The water strikes the ocean at the point  (10   3, 0).   (a) Find the standard form of the equation that represents the path of the water.       (b) The pipe is moved 28 feet up. Find an equation that represents the path of the water.

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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.