Points of Intersection on the TI-83

Note that the TI-83 and the TI-83 plus have slightly different keys. This page uses the keys associated with the TI-83. The differences are that the TI-83 key is replaced by the TI-83 Plus key, and the TI-83 key is replaced by the TI-83 Plus key.

Example 13 in Chapter 2 Section 4 in the text contains a calculator generated graph of two functions: f(x) = ^–2x + 2
g(x) = 2x² – 4x –2 Earlier, as part of the supporting material for Example 14 from Chapter 1 section 2, the book and the web page 128301.htm demonstrated the use of the intersect operation for locating the point of intersection for two functions. We continue that demonstration here, using the two functions from Example 13.

Please note that the calculator used to produce the graphs on this page had just been used to produce the graphs and screen images from the web page 238301.htm. As a result there is some residual material on this calculator.

Figure 1 Figure 1 is taken from the Y= screen on a TI-83 after we have defined the two functions. The first function is a straight line, and the second is a quadratic which will be graphed as a parabola.
Figure 2 Pressing moves the display to Figure 2. Here we see some unexpected items. For one thing, the graph shows a number of points that are not related to this problem at all. Second, the graph of the parabola is made up of separated points. And, third, the WINDOW settings for the graph are not obvious.

Figure 3 To make the parabola appear as connected points, we use the key. This will open the options screen shown in Figure 3. The Dot option needs to be changed. We use the to move the highlight down to the Connected option and then press to selct that option. The result is shown in Figure 4.

Figure 4 Now that the option is set as we want it, we press to redraw the graph.

Figure 5 Here the parabola is connected, but we still have those plotted points left over from some earlier work, and the WINDOW limits are not clear. We will use the ZOOM feature to set the WINDOW ranges to a more standard setting. Press to open the ZOOM menu.

Figure 6 We press to choose ZStandard. This will produce a graph that is different from the one in the text, but it will serve our purpose here, namely, find the points of intersection for the two functions.

Figure 7 The standard window settings gie us a better view of the line and of the parabola. With the new window settings, only two of the plotted points are visible on the screen. To clear those points we need to turn off the statistical plot. To do that we move to the STAT PLOT menu. Press the key.

Figure 8 Now we can see that Plot1 is indeed On. The easiest remedy will be to turn off all of the plots. We do this by using the key to select PlotsOff. That option causes the PlotsOff command to be pasted onto the base window in Figure 9.

Figure 9 Once the command has been pasted onto the window, we press to perform it. The calcualtor responds with Done.
Then, we return to the graph by pressing .

Figure 10 In Figure 10 we finally see the graph without the distracting plotted points.
Our purpose here is to use the intersect command to find the two points of intersection. We could modify the WINDOW settings to have the graph come close to the one presented in the text, but that will not be necessary.

Figure 11 To get to the intersect option we need to use to make the CALC menu appear in the screen. Then, we can press to select the desired item.

Figure 12 intersect goes through a number of steps. First, we need to choose the two curves to use. It is possible that we would have more than 2 curves graphed at the same time. The calculator wants us to choose the two graphs to use. This seems a bit superfluous here given that there are only two functions on this graph. However, we will have to play along with the calcualtor.
The TI-83 is proposing the first function as one of the two curves. We press to accept that choice.

Figure 13 In Figure 13 the TI-83 proposes the second function as the the second curve. Again, press to accept that choice.

Figure 14 Now the calculator is asking for a Guess, and it is proposing the point (0,^–2) as such a guess. We want to be sure that the calculator finds the left point of intersection. Therefore, we will improve the guess to help the calculator. We do this by pressing the key to move the Guess closer to the point of intersection.

Figure 15 In Figure 15 we have a Guess that is reasonably close to the left point of intersection. We press to accept that point and have the calculator do the rest of the work.

Figure 16 The TI-83 has determined that the left point of intersection is (^–1,4).
Now we want to obtain the coordinates of the other point of intersection. To do this we step through the same sequence of screens, but changing our Guess so that it is close to the right point of intersection.

Figure 17 To return to the intersect option we use . This will make the CALC menu appear. Again, we select intersect via the key.

Figure 18 The calculator proposes the first curve as one of the two curves to use. We use the key to accept that choice.

Figure 19 The calculator proposes the second curve as the other curve to use. We use the key to accept that choice.

Figure 20 The TI-83 proposes a point to use as the Guess. We do not want to use that guess because it is too close to the left point of intersection. Therefore, we will use the to shift the guess close to the right point of intersection.

Figure 21 In Figure 21 the new Guess point has been set. Press to accept that value.

Figure 22 intersect has done its work. The right point of intersection is identified as (2,^–2).

Figure 1	Figure 1 is taken from the Y= screen on a TI-83 after we have defined the two functions. The first function is a straight line, and the second is a quadratic which will be graphed as a parabola.
Figure 2	Pressing moves the display to Figure 2. Here we see some unexpected items. For one thing, the graph shows a number of points that are not related to this problem at all. Second, the graph of the parabola is made up of separated points. And, third, the WINDOW settings for the graph are not obvious.
Figure 3	To make the parabola appear as connected points, we use the key. This will open the options screen shown in Figure 3. The Dot option needs to be changed. We use the to move the highlight down to the Connected option and then press to selct that option. The result is shown in Figure 4.
Figure 4	Now that the option is set as we want it, we press to redraw the graph.
Figure 5	Here the parabola is connected, but we still have those plotted points left over from some earlier work, and the WINDOW limits are not clear. We will use the ZOOM feature to set the WINDOW ranges to a more standard setting. Press to open the ZOOM menu.
Figure 6	We press to choose ZStandard. This will produce a graph that is different from the one in the text, but it will serve our purpose here, namely, find the points of intersection for the two functions.
Figure 7	The standard window settings gie us a better view of the line and of the parabola. With the new window settings, only two of the plotted points are visible on the screen. To clear those points we need to turn off the statistical plot. To do that we move to the STAT PLOT menu. Press the key.
Figure 8	Now we can see that Plot1 is indeed On. The easiest remedy will be to turn off all of the plots. We do this by using the key to select PlotsOff. That option causes the PlotsOff command to be pasted onto the base window in Figure 9.
Figure 9	Once the command has been pasted onto the window, we press to perform it. The calcualtor responds with Done. Then, we return to the graph by pressing .
Figure 10	In Figure 10 we finally see the graph without the distracting plotted points. Our purpose here is to use the intersect command to find the two points of intersection. We could modify the WINDOW settings to have the graph come close to the one presented in the text, but that will not be necessary.
Figure 11	To get to the intersect option we need to use to make the CALC menu appear in the screen. Then, we can press to select the desired item.
Figure 12	intersect goes through a number of steps. First, we need to choose the two curves to use. It is possible that we would have more than 2 curves graphed at the same time. The calculator wants us to choose the two graphs to use. This seems a bit superfluous here given that there are only two functions on this graph. However, we will have to play along with the calcualtor. The TI-83 is proposing the first function as one of the two curves. We press to accept that choice.
Figure 13	In Figure 13 the TI-83 proposes the second function as the the second curve. Again, press to accept that choice.
Figure 14	Now the calculator is asking for a Guess, and it is proposing the point (0,^–2) as such a guess. We want to be sure that the calculator finds the left point of intersection. Therefore, we will improve the guess to help the calculator. We do this by pressing the key to move the Guess closer to the point of intersection.
Figure 15	In Figure 15 we have a Guess that is reasonably close to the left point of intersection. We press to accept that point and have the calculator do the rest of the work.
Figure 16	The TI-83 has determined that the left point of intersection is (^–1,4). Now we want to obtain the coordinates of the other point of intersection. To do this we step through the same sequence of screens, but changing our Guess so that it is close to the right point of intersection.
Figure 17	To return to the intersect option we use . This will make the CALC menu appear. Again, we select intersect via the key.
Figure 18	The calculator proposes the first curve as one of the two curves to use. We use the key to accept that choice.
Figure 19	The calculator proposes the second curve as the other curve to use. We use the key to accept that choice.
Figure 20	The TI-83 proposes a point to use as the Guess. We do not want to use that guess because it is too close to the left point of intersection. Therefore, we will use the to shift the guess close to the right point of intersection.
Figure 21	In Figure 21 the new Guess point has been set. Press to accept that value.
Figure 22	intersect has done its work. The right point of intersection is identified as (2,^–2).