### Home > A2C > Chapter 13 > Lesson 13.2.1 > Problem13-100

13-100.
1. Each labeled point on the graph below is either a maximum or a minimum. Homework Help ✎

1. Find the period and amplitude of the graph.

2. Find an equation for the graph.

3. Use one of the labeled points to check your equation.

The horizontal distance can be found by taking the absolute value of the difference in x-coordinates.

The points are one and a half cycles apart. Use 1.5P = horizontal distance.

Use the same technique to find the amplitude. Remember that the amplitude is half of the vertical distance.

Period = 44
Amplitude = 20

y = a cos (b(xh)) + k
where...
a = amplitude
b = # of cycles in 2π
h = horizontal shift
k = vertical shift

$y=3+20\text{cos}\left(\frac{\pi}{22}(x-15)\right)$

See part (b).