NONLINEAR MODELS - For the latter part of the quiz, we will explore some nonlinear models.9. (16pts)QUADRATIC REGRESSIONData:On a particular summer day, the outdoor temperature was recorded at 8 times of the day, and the following tablewas compiled. A scatterplot was produced and the parabola of best fit was determined.t=Timeof day(hour)y= OutdoorTemperature(degrees F.)751960116513661567186520602348Quadratic Polynomial of Best Fit:y= -0.2774t2+ 8.1026t + 8.5794 wheret= Time of day (hour) andy= 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, find themaximum temperature predicted by the quadratic modelandfind thetime when it occurred.Report the time to the nearest quarter hour (i.e., __:00 or __:15 or __:30 or __:45). (Forinstance, 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.
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(b) Use the quadratic polynomial to estimate the outdoor temperature at 6:30 am, to the nearest tenth of adegree. (work optional)
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