Question

A roller coaster is being designed that starts at (0,22) and ends at (19,2),

Along the ride there is a relative minimum at (5,6) and a relative

maximum at (10,18). The roller coaster is almost finished but one

section is missing. Find the correct function that completes the roller

coaster so that the ride is smooth and continuous.

Answer 1

The function is, f(x) = 6·sin((π/5)(x + 3π/2)) + 12

Explanation:

The general form of equation of a roller coaster is given as follows;

y = A·sin(B(x - C)) + D

Where;

A = The amplitude = (18 - 6)/2 = 6

D = The vertical shift = 12

One revolution = 10 unit

∴2·π = 10 unit

Therefore, 10 = 2·π/B

B = 2·π/10

The phase shift = 3·π/2

Therefore, we have the function as follows;

f(x) = 6·sin(2·π/10(x + 3π/2)) + 12 = 6·sin((π/5)(x + 3π/2)) + 12