Graph the function, press 2nd + TRACE, choose 2: Zero, then set a left bound, a right bound, and a guess around the point where the graph crosses the x-axis. The calculator displays the x-value where y = 0.
Does this apply to your TI-84?
Yes, TI-84, TI-84 Plus, and TI-84 Plus CE all use the same CALC menu and Zero function.
What should be set up before I start?
Three things: the calculator should be in Function mode (MODE, then Func), the equation should be entered in the Y= screen, and the graph window should show the point where the graph crosses the x-axis. If you can’t see the crossing, press ZOOM 6 (ZStandard) or adjust the window using the graph window guide.
What is an x-intercept?
An x-intercept is a point where the graph crosses the x-axis, so the y-value there is 0. Those x-values are also the solutions (roots or zeros) of the equation, which is why the calculator’s function for finding them is called Zero.
How do I find the x-intercepts of y = x² − 4, step by step?
- Enter the equation. Press Y=, type
X^2-4in Y1. - Graph it. Press GRAPH. You should see a parabola crossing the x-axis twice.
- Open the CALC menu. Press 2nd, then TRACE.
- Choose Zero. Select 2: zero.
- Set the left bound. The screen asks “Left Bound?” Use the arrow keys to move the cursor to the left of the intercept and press ENTER.
- Set the right bound. The screen asks “Right Bound?” Move the cursor to the right of the same intercept and press ENTER.
- Enter a guess. The screen asks “Guess?” Move the cursor close to the intercept and press ENTER.
- Read the result. The bottom of the screen shows Zero X=-2 Y=0.
- Repeat for the other intercept. Run the same steps with the bounds around the right-hand crossing to get X=2.
How do I read the result?
The calculator shows the x-intercept as X and Y values at the bottom of the screen, with Y equal to 0 (or a number extremely close to 0). The intercept point is (X, 0), so for this example the x-intercepts are (-2, 0) and (2, 0). Each bounded search finds one zero at a time, so a graph with two crossings needs two runs.
Is there another way to find x-intercepts?
Yes. Use the table feature: enter the function in Y=, open the table (2nd + GRAPH), and scroll to the row where Y1 is 0. This is quick when the zero is a whole number. The table feature guide shows how to set the start and step values. For zeros that aren’t whole numbers, the Zero function is more accurate.
Common mistakes and how to fix them
The crossing isn’t visible. The window is hiding it. Use ZStandard or widen Xmin and Xmax until the graph crosses the x-axis on screen.
Both bounds are on the same side of the intercept. The left and right bounds must have the crossing between them. Redo the steps and place one bound on each side.
ERROR: NO SIGN CHANGE. The graph doesn’t cross the x-axis between your bounds. Either the bounds missed the crossing or the graph only touches the axis (as in y = x²), in which case use 2nd + TRACE, 3: minimum to find the touching point instead.
The equation was entered incorrectly. A missing exponent or sign error changes the graph. Re-enter the function in Y= and check it against the original.
The equation isn’t set equal to zero. For something like x² = 4x − 3, move everything to one side first (x² − 4x + 3) and graph that, or use the intersect tool on the two sides.
Practice with the online tool
The TI-84 Calculator Tool on this site lets you enter equations, graph them instantly, and practice finding intercepts without a physical calculator.
FAQ
How do I find the x-intercepts of any function on a TI-84?
Enter it in Y=, graph it, and use 2nd + TRACE, 2: zero with a left bound, right bound, and guess for each crossing.
Why does the calculator show a very small number like 1E-13 for Y?
That’s rounding from the numerical search. A value like 1E-13 is effectively 0, so the x-intercept is correct.
Can I find irrational x-intercepts, like √2?
Yes. The Zero function gives a decimal approximation, such as X=1.4142136 for y = x² − 2.
How many x-intercepts can a graph have?
A quadratic can have 0, 1, or 2. Other functions can have more, and you need to run the Zero function once for each crossing you can see.
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