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Home > A2C > Chapter 8 > Lesson 8.2.2 > Problem 8-127


Find an equation for each graph below.    

  1. Use the general equation .
    Determine the value for each of the three parameters.

    First identify a convenient locator point.
    In this case, we will use:

    The value of the point represents the horizontal shift.
    The value of the point represents the vertical shift.

    The amplitude (a) is the distance from the midline to the highest point.
    In this case and the highest point is , so .
    Since the graph increases from the locator point in the same way does, a is positive.

  1. See part (a).
    Pay careful attention to the scale on the -axis when determining and .

  1. If you choose  as your locator point, notice the first cycle of the graph is an inverted sine curve, so the a value will be negative.

    See part (a).

  1. See parts (a) and (c).