Do you need to find where two functions intersect? carry out you have a TI-84 to add calculator by Texas Instruments? If friend answered yes come both of this questions, proceed reading this Instructable. Finding intersection points making use of a TI-84 to add is basic to do and faster than doing therefore by hand, for this reason this is a helpful skill to know if you need to save time or want to check your work. No special an abilities beyond simple math understanding are required. Time forced to find all intersection points will certainly vary depending on the intricacy of the equations that should be entered and how plenty of points have to be found. For two basic equations with only one intersecting point, detect the intersecting suggest will take around two minutes.

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Materials needed:

1. TI-84 add to calculator

2. 2 intersecting functions

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Step 1: go into the Functions


1. Press ON.

2. Press Y=.

3. Making use of a mix of the scientific calculator keys and also editing keys, get in one that the equations right into Y1.

Note: it does not issue which equation you enter as Y1 and also which is gone into as Y2.

4. Hit the down arrow.

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


Optional: The following steps are optional and are draft to aid you differentiate between your 2 functions.These procedures will interlocutor the Y2 role on the viewing display when the graph is shown.

1. Press the left arrow key until the cursor is blinking on top of the very first character in the Y2 equation.

2. Hit the left arrow key twice.

3. Push the ENTER switch once.

Note: The flashing symbol to the left of the Y2 should now be a bolded line and also should look favor the photo shown above. If ENTER to be hit much more than once, keep pushing ENTER until you have scrolled v all obtainable options and until the bolded line is shown.

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Step 2: pick a Window


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

2. Choose the Xmin, Xmax, and Xscl values.

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

3. Choose the Ymin, Ymax, and Yscl values.

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

4. Pick Xres value.

Note: Xres is the speed that the graph is plotted at. The higher the value, the faster the graph will certainly be plotted. However, higher values likewise decrease the amount of clues plotted i beg your pardon decreases the precision the the curves shown. Worths from 2-4 space recommended.

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Step 3: Graph the Functions


1. Push the GRAPH button.

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

Note: Make sure that all intersecting components are clearly displayed top top the the town hall Screen. You should be able to plainly see where the two functions intersect. If functions intersect in places that are much apart, an interpretation that gift able to plainly see both intersections in ~ the very same time is no possible, emphasis on one in ~ a time before transforming the window to view one more intersecting point.


Optional: If that is clear that Y1 and Y2 crossing for a an easy numerical value on the X axis, sometimes much more information can be learned by finding the intersection allude using the tables. The complying with steps explain how to usage the tables to discover intersection points.

1. Press 2ND and GRAPH to check out the tables.

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

Note: In the Tables you deserve to manually scroll till you uncover the X worth that you think the Y1 and also Y2 features intersected at. If the worths for Y1 and also Y2 room the same for that worth of X, the features do crossing at the point.

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Step 4: find Intersection Points


1. Push 2ND and TRACE.

2. Hit the down arrow until "5:" is highlighted.

3. Press ENTER.

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

Note: that does not matter which duty you choose as the an initial curve and which role you pick as the 2nd curve.

5. Press ENTER to pick the 2nd curve.

Note: after pressing ENTER in the above step 4, the cursor will instantly switch curves. This means that here you only should press ENTER to confirm the 2nd curve.

6. Making use of the left and also right arrowhead keys, navigate till the flashing cursor is close to the intersection suggest you space interested in.

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

7. Push ENTER.

Note: The intersection point"s works with will be displayed at the bottom the the display screen as shown in the last picture above.

Note: having trouble? check out the Troubleshooting ar in Step 5: Conclusion and also Troubleshooting.

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Step 5: Conclusion and also Troubleshooting

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


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

1. ~ hitting ENTER after the "Guess?" screen, I received an error article that claims "ERR: NO sign CHNG."

This means that the 2 equations did not intersect in the window. Adjust the home window and shot again. If this blog post persists, the attributes may never ever intersect.

2. There is much more than one intersection allude on mine screen and also I keep gaining answers because that the various other one(s).

When picking "Guess?", usage the left and also right arrow keys until the cursor is above the intersection allude you want to know much more about. If this is still no working, change the window so that it is focused on the interested intersection allude (typically by make the home window smaller end the intersection point) and shot again.

3. Mine intersection suggest is the very same as my guess point.

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

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