Find the Zeroes of a Function on TI-83 Plus

You can use the TI-83 Plus graphing calculator to find the zeroes of a function. The zeros of the function y = f(x) are the solutions to the equation f(x) = 0. Because y = 0 at these solutions, these zeros (solutions) are really just the x-coordinates of the x-intercepts of the graph of y = f(x). (An x-intercept is a point where the graph crosses or touches the x-axis.)

To find a zero of a function, perform the following steps:

  1. Graph the function in a viewing window that contains the zeros of the function.

    To get a viewing window containing a zero of the function, that zero must be between Xmin and Xmax and the x-intercept at that zero must be visible on the graph.

  2. Set the Format menu to ExprOn and CoordOn.

  3. Press [2nd][TRACE] to access the Calculate menu.

  4. Press [2] to select the zero option.

  5. If necessary, repeatedly press

    image0.png

    until the appropriate function appears at the top of the screen.

  6. Set the Left Bound for the zero you desire to find.

    To do so, use the

    image1.png

    and

    image2.png

    keys to place the cursor on the graph a little to the left of the zero, and then press [ENTER]. A Left Bound indicator appears at the top of the.

  7. Set the Right Bound for the zero.

    To do so, use the

    image3.png

    and

    image4.png

    keys to place the cursor on the graph a little to the right of the zero, and then press [ENTER]. A Right Bound indicator appears at the top of the screen.

  8. Tell the calculator where you guess the zero is located.

    This guess is necessary because the calculator uses a numerical routine for finding a zero. The routine is an iterative process that requires a seed (guess) to get it started. The closer the seed is to the zero, the faster the routine finds the zero.

    To do this, use the

    image5.png

    and

    image6.png

    keys to place the cursor on the graph as close to the zero as possible, and then press [ENTER]. The value of the zero appears at the bottom of the screen.

    image7.jpg
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