Question

Below is the graph of a trigonometric function. It has a maximum point at (-3,4) and an amplitude of 4.6.

What is the midline of this function?

Answer 1

The calculates equation of the midline of this function is y = -0.6

How to determine the midline of this function?

From the question, we have the following parameters that can be used in our computation:

Maximum point = (-3, 4)

Amplitude = 4.6

The midline of this function is represented as

MIdline, y = y-coordinates of the Maximum point - Amplitude

Substitute the known values into the equation

y = 4 - 4.6

Evaluate

y = -0.6

Hence, the midline of this function is y = -0.6

Answer 2

Midline is
`d=-0.6`

Final equation is
`f(x)=4.6cos(x+3)-0.6`

Explanation:

General Sinusodal Function

`f(x)=a*cos(bx+c)+d`

• Amplitude:
  `a`
• Period:
  `(2\pi)/(|b|)`
• Phase Shift:
  `-(c)/(b)`
• Midline:
  `Max-a=d`

Given Information

• Amplitude:
  `a=4.6`
• Period:
  `(2\pi)/(|b|)=(2\pi)/(|1|)=(2\pi)/(1)=2\pi`
• Phase Shift:
  `-(c)/(b)= -(-3)/(1)=-(-3)=3`
• Midline:
  `d=Max-a=4-4.6=-0.6`

Final equation

`f(x)=4.6cos(x+3)-0.6`