### Home > PC > Chapter 6 > Lesson 6.4.1 > Problem6-141

6-141.

Find a cosine function that has a maximum at $\left(2, 5\right)$ and a minimum at $\left(4, 2\right)$.

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

Vertical shift: Since the minimum point is at $y = 2$ and the amplitude is $1.5$, the vertical shift would be their sum.

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

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 $b$.