The loft in Casa Batlló in Barcelona, contains a series of sixty catenary arches which closely resemble parabolas. The left side of the arch is close to parabolic in shape all the way to the floor. On the righ side of the arch, it is parabolic in shape until 2.09 meters from the floor. Then the arch drops vertically at this point. The equation of the parabola that closely models these arches is 17 (y - 2.96) 2, where x and y are measured in meters. %3D 100 How tall is the arch? meters How wide is the floor? meters

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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.