Find the quadratic equation for the height of the arch of a bridge using the flowing facts: the horizontal length of the arch (from side to side) is 1000 feet, the lowest part of the arch (on the far left and far right) is 300 feet high, and the highest part of the arch (in the center) is 1200 feet high. Let x be the horizontal distance from the highest part of the arch and y be the height of the arch. The equation is in the form y = ax? + b: What is the value of a? Give answer to four decimal places. What is the value of b?

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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.