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10-13.

Write a possible equation for each graph. Homework Help ✎

  1. graph a

    Use the general equation .
    Determine the value for each of the four parameters.

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

    Since our point is on the midline, we will use the sine function.
    The -value of the point also represents the horizontal shift:

    Next find , the vertical shift.
    The graph has a midline at (the -axis).
    The parameter is the distance that midline is shifted vertically.
    In this case .

    The amplitude () 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, is positive.

    You will learn more about the parameter in future lessons.
    For now, know that since the distance from the beginning to the end of one cycle is .

  1. graph b

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

  1. graph c

    notice the first cycle of the graph is an inverted sine curve, so the -value will be negative.

    See part (a).

  1. graph d

    See parts (a) and (c).