Can someone help me write an equation for a graph as shown in the image, midline 1 period 4 amplitude 2

Midline:1

Amplitude: 2

Period: 4

Step-by-step explanation:

Equation of a Cosine

The general equati of of the cosine is

With the following parameters:

A=Amplitude or half the length from the maximum to the minimum values

w=angular frequency (rad/sec)

=phase shift (rad or degrees)

M=Midline of vertical shift.

The cosine and the sine are both sinusoid functions but we have chosen the cosine as the selected function because its value is maximum when x=0, just like the graph shown in the question.

It can be seen that the maximum value is 3 and the minimum value is -1. That gives us the amplitude:

The midline can be found as the displacement from the center of the wave. Since the maximum value is 3 and the amplitude is 2, the midline is

The general equation is now

To compute the phase shift and the angular frequency, we take two points from the graph: (0,3) (4,3). Let's plug in both values:

Solving

The equation is now

Now for the next point

2cos(4w)=2

cos(4w)=1

The solution for the equation cannot be an angle of 0, we go forward to the next angle where the cosine is 1

Or, equivalently

The period is given by

The equation of the function is