1. Marble Arch in London is a monument with three arches - one large and two smaller. The smaller arches are each 3.66m high at their apex and 1.83 wide at the base. By modelling these arches as parabolas, taking the bottom left point of the arch to be (0, 0), find an equation describing the arch. When on parade, the highest point of the standard carried by a man on horseback is 2.8m above the ground. If the standard would pass 30cm horizontally from the left- most point of the arch, would it fit underneath?

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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.