Find the formula for a function of the form y=Asin(Bx)+C with a maximum at (1.5,1), a minimum at (4.5,−11), and no critical points between these two points.

Answer 1

1/2 period is 4.5-1.5 = 3
so you will have sin((π/3)x)
The center line is at y = (1-11)/2 = -5
the amplitude is (1+11)/2 = 6
so you have 6sin(π/3 x)-5
But, y=0 at x = (1.5+4.5)/2 = 3
so you have y = 6sin(π/3 (x-3))-5
But, y is falling there, instead of rising, so
y = -6sin(π/3 (x-3))-5