# How to Find the Intersection of a Graph on a Ti-84 Graphing Calculator

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On a regular basis, math and physics problems require a graphing calculator to find the intersection point of two graphs or the intersection point of a graph with an axis. Attempting to find these points by hand can be tedious and frustrating if possible at all. However, with a TI 83 or TI 84 graphing calculator, it is extremely simple and takes only a few moments of typing and utilizing the built-in functions of the calculator.

## Finding the Intersection Point of Two Graphs

• Press "Y=" the blue button at the top left of the calculator. A screen will appear with the cursor after "Y1=." Type in the first equation and press "ENTER." The cursor will move to "Y2=." Type in the second equation and press "ENTER" followed by "GRAPH," the blue button at the top right of the calculator. Your graphs will appear on the screen.

• Press "2nd" (the yellow button on the left), followed by "TRACE" (the fourth blue button at the top). Press the down arrow until "intersect" is highlighted and press "ENTER." A blinking box will appear on one of your graphs and the calculator will ask, "First Curve?"

• Press "ENTER." The box will move to the second graph and ask "Second curve?" Press "ENTER" again. The box will not move and the calculator will ask "Guess?"

• Use the left and right arrow keys to move the box close to the intersection point and press "ENTER." The calculator will display "Intersection x= y=" with x and y followed by the values of the intersection point.

## Finding the Intersection of a Graph With the X-axis

• Press "Y=" the blue button at the top left of the calculator. A screen will appear with the cursor after "Y1=." Type in the equation and press "ENTER" followed by "GRAPH," the blue button at the top right of the calculator. Your graph will appear on the screen.

• Press "2nd" (the yellow button on the left), followed by "TRACE" (the fourth blue button at the top). Press the down arrow until "zero" is highlighted and press "ENTER." A blinking box will appear on your graph and the calculator will ask "Left Bound?"

• Find the point where the graph crosses the x-axis. Use the left and right arrow keys to position the box to the left of this point and press "ENTER." The calculator will ask "Right bound?"

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• Use the left and right arrow keys to position the box to the right of the intersection point and press "ENTER." The calculator will ask "Guess?"

• Use the left and right arrow keys to move the box close to the point where the graph crosses the axis and press "ENTER." The calculator will display "Zero x= y=" with x and y followed by the values of the point where the graph touches the x-axis.

## The Intersection of a Graph With the Y-axis

• Press "Y=" the blue button at the top left of the calculator. A screen will appear with the cursor after "Y1=." Type in the equation and press "ENTER" followed by "GRAPH," the blue button at the top right of the calculator. Your graph will appear on the screen.

• Press "2nd" (the yellow button on the left), followed by "TRACE" (the fourth blue button at the top). Press the down arrow until "value" is highlighted and press "ENTER." Your graph will re-appear with the prompt "X=."

• Type "0" and press "ENTER." A box will appear where your graph crosses the y-axis and your calculator will display "x= y=." The variables x and y will be followed by the values of the point where the graph crosses the axis.

## Tips & Warnings

• Make sure that your "Window" is set so that you can see your graph. Change this by pressing the second blue button at the top of the calculator and entering values for the highest and lowest values shown on each axis.
• Don't be worried if the calculator idles, some graphs take time to calculate. If there is a blinking line in the upper right-hand corner of the screen, your calculator is working and will display the answer shortly.
• If you are finding where a graph crosses the x-axis and you receive the error "NO SIGN CHNG," you did not move the box properly. Be sure that the first point selected is to the left of the intersection, while the second point is to the right of the intersection.

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