The graph of a sinusodial function intersects its midline at (0,-3) and then has a maximum point at (2,-1.5).

Answer 1

A= 1.5, B = 2pi/period =2pi/4 = pi/2, D=-3

f(x) = AsinB(x+C)+D = 1.5sin[(pi/2)(x-C)-3

-3 = 1.5sin[(pi/2)(-C)] -3

sin[(pi/2)(-C) ]= 0

pi/2(-C) = 0

C=0

f(x) = 1.5sin(pix/2)-3