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Each labeled point on the graph below is either a maximum or a minimum.

Repeating wave curve, with first visible high point labeled, (15, comma 23) & last visible low point, labeled  (81, comma negative 17), with one low & one high point in-between.

  1. What are 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. Write an equation for the graph.

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

    Review the Math Notes box in Lesson 9.2.4 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.

  3. 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.