Amplitude Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium

A sinusoidal function has a maximum value of

8

and a minimum value of

2

. Find the amplitude and midline.

Solution

1
Amplitude $= \frac{\text{max} - \text{min}}{2} = \frac{8 - 2}{2} = 3$ .
2
Midline $= \frac{\text{max} + \text{min}}{2} = \frac{8 + 2}{2} = 5$ , so $y = 5$ .

Answer

\text{Amplitude} = 3, \quad \text{Midline: } y = 5

When given the maximum and minimum values of a sinusoidal function, the amplitude is half the total vertical range and the midline is the average of the extreme values. This allows you to determine