Let P (x.y) be a point on the graph of y = x2-3 (a) Express the distance d from P to the origin as a function of x. d(x)x4 - 5x2 9 (b) What is d if x = 0? d(0) 3 (Round to two decimal places.) (c) What is d if x = 1? d(1) 2.24 (Round to two decimal places.) Use a graphing utility to graph d d(x) in order to answer the following question (d) For what positive value of x is d smallest? (Round to two decimal places.)

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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.