Final answer:
The sinusoidal function based on the given points (0, -3) and (1, 1) is y = 2 sin(π/2 x) - 3 with an amplitude of 2, vertical shift of -3, no phase shift, and an angular frequency of π/2.
Step-by-step explanation:
To find the equation of the sinusoidal function given the minimum point and the intercept with the midline, we need to determine four parameters: amplitude (A), vertical shift (D), phase shift (C), and the angular frequency or period (B). Since the minimum point is at (0, -3), this gives us the value of D -3, because this will be the vertical shift from the midline to the minimum. The graph intersects the midline at (1,1), indicating that after one unit from the minimum, the sinusoidal wave reaches the midline, which is also the horizontal shift C. The vertical distance between the midline and the minimum is 1 - (-3) = 4, which is twice the amplitude, yielding an amplitude of A = 2.
To find the angular frequency, we consider that the midline is reached after a quarter of the period, so the period T must be 4 units of x. Since the period and angular frequency are related by T = (2π)/B, we can solve for B by rearranging the formula: B = (2π)/T, producing B = π/2. The resulting sinusoidal function is y = A sin(B(x - C)) + D, so the equation of the wave function is y = 2 sin(π/2 x) - 3.