The equation yˆ=-0.37x2+6.15x+52.3 approximates the average temperature in October in degrees Fahrenheit at an agricultural community x hours after 5 a. m. What is the best estimate for the average temperature in October at 10 a. m.?

The best estimate for the average temperature in October at 10 a. m. is 73.8 degrees Fahrenheit.

Solution:

Number of hours after 5 a. m.: x

At 10 a. m.→x=10-5→x=5

yˆ=-0.37 (5) ^2+6.15 (5) + 52.3

yˆ=-0.37 (25) + 30.75+52.3

yˆ=-9.25+30.75+52.3

yˆ=73.8

Answer: The best estimate for the average temperature in October at 10 a. m. is 73.8 degrees Fahrenheit.