The distance between the towers of the main span of the Golden Gate Bridge is about 1280m; the sag of the cable halfway between the towers on a cold winter day is about 143m. (a) How long is the cable, assuming it has an approximately parabolic shape? (HINT: Represent the cable as a parabola of the form y = kx2 and determine k to at least 1 decimal place.)  I got 1321.38m. is that correct?

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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.