Question

Fill out the following chart to find the temperatures for t = 12 (noon) and t = 24 (midnight). (2 points: 1 point for each row) t

C(t) = –0.30(t – 12)2 + 40


0


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 points: 2 points for correct coordinates, 1 point for correct shape)



Convert the Function to Degrees Fahrenheit:

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)? (2 points: 1 point for each transformation)

Note: The conversion rule for Celsius to Fahrenheit is F(t)=9/5C(t)+32

Answer 1

Part.1
Given equation:
C(t) = -0.30 (t – 12)² + 40

For t = 0
C(t) = -0.30 (0 - 12)² + 40
C(t) = -0.30 (-12)² + 40
C(t) = -3.2


For t = 12 (noon)
C(t) = -0.30 (12 - 12)² + 40
C(t) = -0.30 (0)² + 40
C(t) = 40

For t = 24 (midnight)
C(t) = -0.30 (24 - 12)² + 40
C(t) = -0.30 (12)² + 40
C(t) = -0.30 × 144 + 40
C(t) = - 43.2 + 40
C(t) = -3.2

Part.2
Graph of the equation is given in the attachment.

Part.3
C(t) = –0.30(t – 12)² + 40
F(t)=9/5C(t)+32

Substituting the values:
F(t)=9/5{–0.30 (t – 12)² + 40}+32
F(t) = -0.54 (t – 12)² + 72 + 32
F(t) = -0.54 (t – 12)² + 104