Watch VideoShow ExamplesWrite a cosine function that has an amplitude of 4, a midline of y, equals, 5y=5 and a period of one quarter 41​ .

The general form of a cosine function is y = A cos(B(x - C)) + D, where:

• A is the amplitude
• B is the frequency, which is related to the period by the formula B = 2π / period
• C is the phase shift, which tells you how much the graph is shifted horizontally
• D is the vertical shift, which tells you how much the graph is shifted vertically

Given that the amplitude is 4, the midline is y = 5, and the period is 1/4, we can plug these values into the general form to get our specific cosine function.

The amplitude of 4 tells us that A = 4.

The midline of y = 5 tells us that D = 5.

The period of 1/4 tells us that B = 2π / (1/4) = 8π.

Since no phase shift is mentioned, we can assume C = 0.

So, the cosine function that meets these criteria is y = 4 cos(8πx) + 5.