On a particular fall day, the outdoor temperature was recorded periodically and a quadratic function was...

 

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On a particular fall day, the outdoor temperature was recorded periodically and a quadratic function was used to model the data. y=f(t)=-0.3+9.71-2 for 4 st 22 where t = time of day (in hours) and y temperature (in degrees) REMARK: Time is measured in hours elapsed since midnight. For instance, t=4 means 4 am. t=22 means 10 pm. (a) Using algebraic techniques we have learned, find the maximum temperature predicted by the quadratic model and find the time when it occurred. Report the time to the nearest half hour (i.e.,:00 or :30). (For instance, a time of 18.5 hours is reported as 6:30 pm in the usual time notation.) Report the maximum temperature to the nearest tenth of a degree. Show algebraic work. (b) Find and interpret the average rate of change off over the interval [6, 12]. Show work. (c) Use the quadratic polynomial y = -0.31 +9.7t-2 together with algebra to approximate the time(s) of day when the outdoor temperature y was 60 degrees. That is, solve the quadratic equation 60 = -0.312 +9.71-2. Show work in solving. (Show how the quadratic formula is used, with the appropriate values substituted.) Round the results to the nearest tenth. Write a concluding sentence to report the time(s) to the nearest half-hour, in the usual time notation. On a particular fall day, the outdoor temperature was recorded periodically and a quadratic function was used to model the data. y=f(t)=-0.3+9.71-2 for 4 st 22 where t = time of day (in hours) and y temperature (in degrees) REMARK: Time is measured in hours elapsed since midnight. For instance, t=4 means 4 am. t=22 means 10 pm. (a) Using algebraic techniques we have learned, find the maximum temperature predicted by the quadratic model and find the time when it occurred. Report the time to the nearest half hour (i.e.,:00 or :30). (For instance, a time of 18.5 hours is reported as 6:30 pm in the usual time notation.) Report the maximum temperature to the nearest tenth of a degree. Show algebraic work. (b) Find and interpret the average rate of change off over the interval [6, 12]. Show work. (c) Use the quadratic polynomial y = -0.31 +9.7t-2 together with algebra to approximate the time(s) of day when the outdoor temperature y was 60 degrees. That is, solve the quadratic equation 60 = -0.312 +9.71-2. Show work in solving. (Show how the quadratic formula is used, with the appropriate values substituted.) Round the results to the nearest tenth. Write a concluding sentence to report the time(s) to the nearest half-hour, in the usual time notation.