9. (16 pts) QUADRATIC REGRESSION Data: On a particular summer day, the outdoor temperature was recorded at 8 times of the day, and the following table was compiled. A scatterplot was produced and the parabola of best t was determined. Temperature y= Outdoor on a Summer Day Temperature 90 80 new; 1; ftx)=0.3 . mm 52 in 70 R1 = 3}." 67 E, 60 73 E 50 76 E 40 E 30 78 E. 20 79 a 10 76 o 61 o 4 s 12 16 2 24 Time of Day {hour} Quadratic Polynomial of Best Fit: y = -0.3476t2 + 10.948t - 6.0778 where t 2 Time of day (hour) and y 2 Temperature (in degrees) REMARKS: The times are the hours since midnight. For instance, 7 means 7 am, and 13 means 1 pm. (a) Using algebraic techniques we have learned, nd the maximum temperature predicted by the quadratic model and find the time when it occurred. Report the time to the nearest quarter hour (Le, :00 or :15 or :30 or :45). (For instance, a time of 18.25 hours is reported as 6:15 pm.) Report the maximum temperature to the nearest tenth of a degree. Show algebraic work. (b) Use the quadratic polynomial to estimate the outdoor temperature at 7:30 am, to the nearest tenth of a degree. (work optional)