Welcome to Oakville Lake Amusement Park! As one of the new rollercoaster engineers, you have been tasked with developing a rollercoaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the rollercoaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground. There must be three distinct points where the rollercoaster crosses the x–axis. Precise measurements and attention to detail are very important. First, here is the existing map of current structures. It is important that the rollercoaster does not go through the foundation of any of these structures. Pick three points on the x–axis that the rollercoaster will dive underground or resurface. (Points that have a building on them are off-limits.) 1. The rollercoaster will run from right to left, so work in that order when selecting points. 1st point:___-8___ 2nd point:___-2___ 3rd point:___6___ 2. Using those points as zeros, construct the polynomial function, f(x), that will be the path of your rollercoaster. Show all of your work. 3. Using two of the theorems dicussed in the lesson, prove to the construction foreman that your function matches your graph. Use complete sentences. 4. Solve for the y–intercept for your function, f(x), and then construct a rough graph of your rollercoaster. If your y–intercept is off the graph, give the coordinates of the y–intercept. 5. Two competing engineers have offered their solutions for the function. One has suggested g(x) = x3 – 2x2+ 4x – 8, and the other has suggested h(x) = x3 + 5x2 – 8x – 48. Explain to the C.E.O. of Oaville Lake Amusement Park why these other suggestions are invalid. Use complete sentences.