CPM Homework Banner
10-13.

Write a possible equation for each graph.

  1. Repeating wave curve, first visible, low & high points: (negative pi fourths, comma 1) & (3 pi fourths, comma 3), continuing to repeat the wave, with the following highlighted points: (pi fourths, comma 2), (5 pi fourths, & (9 pi fourths, comma 2).

    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. Repeating wave curve, first visible, low & high points: (negative pi , comma negative 1) & (0, comma 1), continuing to repeat the wave, with the following highlighted points: (negative pi halves, comma 1 half), & (pi halves, comma 1 half).

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

  1. Repeating wave curve, first visible low & high points: (negative 3 pi fourths, comma 1) & (negative pi thirds, comma 3), continuing to repeat the wave, with the following highlighted points: (negative 5 pi sixths, comma 2),  (pi sixth, comma 2), & (7 pi sixth, comma 2).

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

    See part (a).

  1. Repeating wave curve, first visible high & low points: (negative 5 pi sixths, comma 2) & (pi sixths, comma negative 4), continuing to repeat the wave, with the following highlighted points: (negative pi thirds, comma negative 1),  (2 pi thirds, comma negative 1), & (5 pi thirds, comma negative 1).

    See parts (a) and (c).