### Home > CCA2 > Chapter 12 > Lesson 12.2.1 > Problem12-98

12-98.

Each labeled point on the graph at right is either a maximum or a minimum. Homework Help ✎

1. Find the period and amplitude of the graph.

Period: How far is it between consecutive maximums or minimums?
Amplitude: How “tall” is the graph? Divide this answer by $2$.

1. Find an equation for the graph.

Find the vertical and horizontal shifts. For the vertical shift, what number is in the middle of 23 and −17?

Review the Math Notes box in Lesson 7.2.4 for help with the general equation of a sine or cosine graph.
In this case, it is more convenient to use cosine because you know a maximum point.

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

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

Substitute the values for each of the points into the equation to verify that it is correct.