WA
The midline is y=
The amplitude is
The period is

The midline is y=-1

Amplitude = 3

The period is 2 units

Step-by-step explanation:

Sinusoidal Function

It refers to a mathematical curve with a smooth and periodic oscillation. Its name comes from the sine function but it can be a cosine function too. They only differ by the phase angle of 90 degrees or π/2 radians.

The amplitude is half the distance from the maximum and the minimum points. The graph shows a sinusoid with a maximum value of y=2 and a minimum value of y=-4.

The amplitude is:

Amplitude = 3

The midline is the distance from the center of the sinusoid to the x-axis. It's also called the vertical shift.

The midline can be found by subtracting the amplitude A=3 to the maximum value M=2:

ML = 2 - 3 = -1

It can also be found by adding the amplitude to the minimum value:

ML = -4 + 3 = -1

The midline is y=-1

The period is the time the wave takes to complete a full cycle. We only have to focus at any point on the wave (xo,yo) and find the next value of x where the sinusoid has the very same behavior (x1,y1). The period is then x1-x0.

We find at x=0, y=-1 and it's moving up. At x=1 it has the same value but it goes down, so the wave is at its half cycle. At x=2 it repeats the same behavior as for x=0. Thus:

The period is 2 units