Temperature in the desert can be modeled by the function C(t), where t represents hours after midnight (0 ≤ t ≤ 24), and C is the temperature measured in degrees Celsius. Examine what happens to the graph when you transform the function to degrees Fahrenheit. 1. Fill out the following chart to find the temperatures for t = 12 (noon) and t = 24 (midnight). (2 points: 1 point for each row)
0: C(0) = -0.30(0 - 12)^2 + 40
C(0) = -0.30(144)+40
C(0) = -43.2 + 40
C(0) = -3.2 °C
12:
24:

2. Plot the three points from the chart onto the graph below. Use the plotted points to sketch the graph of C(t) = –0.30(t – 12)2 + 40.

3. Suppose you want to represent the desert temperature in degrees Fahrenheit instead. How would you transform the function C(t) to make the new function, F(t)?

4. Take your values from the previous chart (in question 2) and convert them from Celsius to Fahrenheit. Follow the example below, and use the conversion rule to fill out the chart for degrees Fahrenheit when t = 12 and t = 24.

5. Use the conversion formula to write the equation for the new function, F(t).

6. Plot the points from the Fahrenheit chart in question 4 onto the graph below. Use the plotted points to sketch out the graph of F(t).

7. Compare the graph in question 6 (F(t)) with the graph in question 2 (C(t)). What changes were made to the graph of C(t) to transform it to F(t)?