Amplitude Math Example 2

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Example 2

medium
Find the amplitude and midline of g(x)=−3cos⁡(2x)+4g(x) = -3\cos(2x) + 4.

Solution

  1. 1
    The amplitude is ∣A∣=∣−3∣=3|A| = |-3| = 3.
  2. 2
    The midline (vertical shift) is y=D=4y = D = 4.
  3. 3
    The maximum value is D+∣A∣=4+3=7D + |A| = 4 + 3 = 7 and the minimum is D−∣A∣=4−3=1D - |A| = 4 - 3 = 1.

Answer

Amplitude=3,Midline: y=4\text{Amplitude} = 3, \quad \text{Midline: } y = 4
The negative sign in front of the coefficient reflects the graph but does not change the amplitude. Amplitude is always positive (it is the absolute value of AA). The midline y=Dy = D is the horizontal line about which the function oscillates.

About Amplitude

Amplitude is the maximum vertical distance from the midline of a periodic function to a peak or trough.

Learn more about Amplitude →

More Amplitude Examples

Example 1 easy

Find the amplitude of [formula].

Example 3 medium

A sinusoidal function has a maximum value of [formula] and a minimum value of [formula]. Find the am

Example 4 hard

Write the equation of a cosine function with amplitude [formula], period [formula], midline [formula

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