Arches like the S aint Lo uis Gate w ay A rch are not parabolas. Ray’s company has been hired to set up a concert stage approximately 15 feet from one base of the arch. One of the bands that will be performing uses a 30-foot tall guitar as one of its props, and Ray is worried that it will not fit under the arch. He adds coordinate axes to the drawing above to model the Gateway Arch, where both x and y represent distance in feet and the origin is the point on the ground directly below the arch’s ap ex (its highest point). He knows that the arch is 630 feet wide and 630 feet tall. Use the problems below to help Ray decide if he should be worried.
a. Help Ray write a function to model the height of the arch relative to the horizontal position from the center.
b. How tall is the arch 15 feet from its base? Should Ray be worried?
c. What is a useful domain for this model of the St. Lo uis G ate way Ar ch?