Using a calculator or a computer,plot the parabola f(x).Compare this to your originally sketch in part a. by noting any similarities or differences

wyzant Ask An Expert Q. Search ) Find an Online Project: Explain the mathematics of roller coaster construction, Imagine you are a roller coaster designer, and are asked to mathematically represent the curve of the first drop of a new ride. Bly looking at some of your favorite coasters, you determine that the optimal slope for the ascent. when the car is being pulled up the slope by a chain, is 0.7. The slope of the first drop that will be the most thrilling (without being dangerous) is -1.5. You decide to connect these two straight stretches, y = LI and y = 12, with a parabola of the form y = f() = ax 2 + bx . c. where x and fug are measured in meters. In order for the curve of the track to remain smooth, you must make sure that the linear segments, L 1 and 12 , have the same slope at each endpoint of the parabola, points P and O. This ensures that the parabola is differentiable, as well as continuous at the endpoints Choose point P. the left endpoint of your parabola, as your origin, to simplify calculations Draw a rough sketch of LI with slope 0.7, ending at point P. Then sketch L2 with slope -1.5. atting at point Q a short distance to the right and below point P. Finally, sketch the parabola that connect P and Q while matching the slopes of LI and L2 al distance between P and Q is 40 meters, write equations in