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?

Time (minutes) amount of water (gallons) practice 1. jin fills up a 510-gallon pool in the backyard for her children. she fills it with the garden hose at a rate of 17 gallons per minute. after it is filled, she lets it sit for 30 minutes in order to let the water temperature rise. the children then get in and have fun for an hour. the pool loses about 5 gallon of water each minute due to their splashing and playing. at the end of the hour, they tear the pool while getting out, which causes a leak the pool then begins to lose water at a rate of 2 gallons per minute. a. complete the table to show the amount of water in the pool after each minute. b. create a graph to model the problem situation. include when the pool will be empty. c. write a piecewise function that models this problem situation. explain your reasoning for each piece of the function. d. identify the x- and y-intercept. explain what they mean in terms of the problem situation, atamantha a cul 80 100 120 150 200 ning, inc