In testing a new automobile braking system, engineers recorded the speed x (in miles per hour) and the stopping distance y (in feet). The table shows the results.

(a) Find the least squares regression parabola y = ax2 + bc + c for the data by solving the system.

(b) Use a graphing utility to graph the model you found in part (a) and the data in the same viewing window. How well does the model fit the data? Explain.
(c) Use the model to estimate the stopping distance when the speed is 75 miles per hour.

30 | 40 | 50 | 60 | 70 Stopping Distance, y | 75 | 118 | 175 | 240 | 315 Speed, x 923 5c + 250b + 13,500a 250c + 13,500b + 775,000a 52,170 13,500c + 775,000b + 46590000a = 3,101,300