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Question 1039985: Hi there, I'm having some difficulty on this problem. I have some it worked out, but I could use some guidance please!:
QUADRATIC REGRESSION
Data: On a particular spring day, the outdoor temperature was recorded at 8 times of the day. The parabola of best fit was determined using the data.
Quadratic Polynomial of Best Fit:
y = -0.2t^2 + 6.3t + 42.9 for 0 less than or equal to t less than or equal to 24 where t = time of day (in hours) and y = temperature (in degrees)
REMARKS: The times are the hours since midnight.
For instance, t = 6 means 6 am. t = 22 means 10 pm. t = 18.25 hours means 6:15 pm
(a) Use the quadratic polynomial to estimate the outdoor temperature at 6:30 am, to the nearest tenth of a degree. (work optional)
75.4
(b) 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 quarter hour (i.e., __: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.
I'm not sure how to do this part.
c) Use the quadratic polynomial y = -0.2t^2 + 6.3t + 42.9 together with algebra to estimate the time(s) of day when the outdoor temperature y was 82 degrees.
That is, solve the quadratic equation 82 = -0.2t^2 + 6.3t + 42.9.
Show algebraic work in solving. Round the results to the nearest tenth. Write a concluding sentence to report the time(s) to the nearest quarter-hour, in the usual time notation. (Use more paper if needed)
Any help is greatly appreciated!
Answer by josgarithmetic(39618)   (Show Source):
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