CPM Homework Help : PC3 Problem 10-12

Write the equation of a cosine function that has a maximum at $(2, 5)$ and a minimum at $(4, 2)$ .

Hint 1:

$\text{amplitude}= \:\frac{\text{max }-\text{ min}}{2}$

Hint 2:

$\text{vertical shift}= \:\frac{\text{max }+\text{ min}}{2}$

Hint 3:

Horizontal shift: Since the maximum point is at (2, 5) a cosine function has been shifted 2 units right.

Hint 4:

Since a maximum is at $x = 2$ and a minimum is at $x = 4$ , half of a cycle is $2$ units. Hence, the period is $4$ .
Use the formula $pb = 2π$ to calculate $b$ .