A bowl is designed so that it has a vertical cross-section in the shape of a parabola. The width of the bowl at its opening is 38 centimeters, and the depth of the bowl is 10 centimeters. Assuming that the base of the bowl is represented by the point (0,0), find the equation of a parabola that represents the shape of the bowl.

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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.