Do you need to find where two functions intersect? perform you have a TI-84 add to calculator through Texas Instruments? If you answered yes come both of these questions, proceed reading this Instructable. Detect intersection points using a TI-84 add to is basic to do and faster than doing for this reason by hand, so this is a helpful skill to understand if you should save time or want to check your work. No special an abilities beyond an easy math understanding are required. Time forced to uncover all intersection points will vary depending on the intricacy of the equations that need to be entered and also how numerous points should be found. Because that two straightforward equations with just one intersecting point, detect the intersecting allude will take around two minutes.

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Materials needed:

1. TI-84 add to calculator

2. Two intersecting functions

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Step 1: enter the Functions


1. Press ON.

2. Press Y=.

3. Using a mix of the scientific calculator keys and also editing keys, enter one the the equations right into Y1.

Note: the does not issue which equation you enter as Y1 and which is entered as Y2.

4. Struggle the under arrow.

5. Utilizing a combination of the scientific calculator keys and editing keys, enter the other equation into Y2.


Optional: The following steps are optional and also are draft to assist you differentiate in between your 2 functions.These steps will bolder the Y2 duty on the viewing display screen when the graph is shown.

1. Press the left arrowhead key until the cursor is blinking on height of the first character in the Y2 equation.

2. Fight the left arrow key twice.

3. Press the ENTER button once.

Note: The flashing symbol to the left of the Y2 should now it is in a bolded line and also should look prefer the snapshot shown above. If ENTER was hit more than once, keep pressing ENTER till you have scrolled with all obtainable options and also until the bolded line is shown.

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Step 2: pick a Window


1. Push the WINDOW button on the top row of your TI-84 Plus.

2. Pick the Xmin, Xmax, and also Xscl values.

Note: Xmin is the minimum worth on the X axis, Xmax is the maximum worth on the X axis, and Xscl is the scale that the X axis will be significant with.

3. Pick the Ymin, Ymax, and also Yscl values.

Note: Ymin is the minimum worth on the Y axis, Ymax is the maximum value on the Y axis, and Yscl is the scale that the Y axis will be marked with.

4. Choose Xres value.

Note: Xres is the speed that the graph is plotted at. The greater the value, the faster the graph will be plotted. However, higher values also decrease the quantity of clues plotted which decreases the precision of the curve shown. Values from 2-4 are recommended.

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Step 3: Graph the Functions


1. Push the GRAPH button.

2. If necessary, readjust the window by repeating Step 2: select a Window.

Note: Make sure that all intersecting parts are plainly displayed on the city hall Screen. You should be may be to plainly see wherein the two features intersect. If functions intersect in places that are far apart, definition that gift able to clearly see both intersections at the same time is not possible, focus on one in ~ a time before transforming the home window to view one more intersecting point.


Optional: If the is clear the Y1 and also Y2 intersect for a an easy numerical worth on the X axis, sometimes more information deserve to be learned by finding the intersection point using the tables. The following steps explain how to usage the tables to discover intersection points.

1. Push 2ND and also GRAPH to view the tables.

2. When in the X column, push the up or down arrowhead key come manually scroll until the X value is found.

Note: In the Tables you have the right to manually scroll till you uncover the X worth that you think the Y1 and also Y2 attributes intersected at. If the values for Y1 and also Y2 room the same for that value of X, the features do intersect at the point.

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Step 4: discover Intersection Points


1. Press 2ND and also TRACE.

2. Fight the down arrow till "5:" is highlighted.

3. Push ENTER.

4. Push ENTER again to select the an initial curve.

Note: the does not matter which function you choose as the first curve and also which role you select as the 2nd curve.

5. Push ENTER to select the second curve.

Note: after ~ pressing ENTER in the above step 4, the cursor will instantly switch curves. This method that right here you only have to press ENTER to confirm the second curve.

6. Using the left and also right arrow keys, navigate until the flashing cursor is close to the intersection allude you space interested in.

Note: because that the "Guess?" the cursor location does not should be accurate. However, to make certain that the intersection allude found is the one you space looking for, the cursor should be closer come the intersection point you room interested in than to any kind of other intersection points.

7. Push ENTER.

Note: The intersection point"s coordinates will be shown at the bottom the the display screen as presented in the last snapshot above.

Note: having actually trouble? inspect out the Troubleshooting ar in Step 5: Conclusion and Troubleshooting.

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Step 5: Conclusion and Troubleshooting

If friend found every one of your intersecting points, congratulations! Step 4: discover Intersection Points might be recurring to uncover other intersection clues that space on the exact same screen. To uncover other intersection clues that are not top top the Window, repeat Step 2: pick A Window with Step 4: discover Intersection Points to adjust the home window first.


Troubleshooting: If you"ve had some trouble, right here are a couple of valuable hints:

1. After ~ hitting ENTER after ~ the "Guess?" screen, I obtained an error message that says "ERR: NO sign CHNG."

This method that the two equations did not intersect in the window. Change the window and shot again. If this message persists, the features may never intersect.

2. There is an ext than one intersection allude on mine screen and also I keep gaining answers for the other one(s).

When choosing "Guess?", use the left and right arrow keys till the cursor is over the intersection allude you want to know much more about. If this is still not working, readjust the home window so that it is concentrated on the interested intersection allude (typically by make the window smaller over the intersection point) and try again.

3. My intersection allude is the very same as mine guess point.

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This deserve to be feasible in 2 situations. Case one is the you room very great at guessing. Case two is that the features are the exact same (possibly composed in various ways) which method that every points space technically points whereby the functions intersect. The TI-84 to add starts searching for intersection clues at your "Guess?" point, then spreads out. However, together your "Guess?" suggest is one intersection point, the TI-84 to add will give that as an answer. To examine if the attributes are the same over a selection of numbers, look at the table and compare worths of Y1 and Y2 because that the same values the X (this is described in Step 3: Graph the Functions).

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