Question

The function f(x) will model the roller coaster’s height from the ground in feet over time, measured in seconds since the ride started.

Answer 1

1) 12<x<15 is: f(x) = -5(x-12)^2 + 80

2) 15<x<17 is: f(x) = 35

3) 27<x<30 is: f(x) = 2.5x-22.5

Explanation:

See the attached image.

1) Plot all the lines as shown

2) Add the inequalities, which will produce the colored regions on DESMOS.

3) Assume that the function having the greatest value in each region is the function that determines the roller coaster's height (My assumption - it is not clear in the problem which function should dominate)

4) for the three regions listed with no corresponding function, identify the line having the greatest value. Thiose are the functions that are noted on the graph and in the answer box above.

5) Take a break