TI-84 CALCULATOR GUIDE
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TI-84 Plus CE · Solve an equation with its graph
X² − 5X + 6 = 0
See the keys to press and what your calculator should show before asking about your own problem.
What you should see
The two solutions are X = 2 and X = 3.
Before you start: function mode
Press MODE. Use the arrow keys to select FUNC (Func on some versions) and press ENTER. Press 2nd, then MODE (QUIT) to leave the menu. These examples use ordinary function graphing. Preserve any work you need before changing entries or settings.
1. Graph the expression that should equal zero
In Y=, use an unused enabled line to enter X² − 5X + 6. Preserve your existing work and turn unrelated functions and Plot labels off. For an equation L = R, graph L − R instead.
Y=X,T,θ,nWhat you should see: Your enabled Y line contains X² − 5X + 6.
2. Choose a useful window
In WINDOW, set Xmin = 0, Xmax = 5, Xscl = 1, Ymin = −1, Ymax = 7 and Yscl = 1. Use (-) to enter −1. Press GRAPH.
WINDOWGRAPHWhat you should see: A parabola crosses the x-axis near X = 2 and X = 3.
3. Open the zero tool
Press 2nd, then TRACE to open CALC. Choose 2:zero. If more than one function is enabled, use the up/down arrows to select the intended curve.
2ndTRACE2:zeroWhat you should see: The calculator asks for Left Bound?.
4. Find the first root
For Left Bound?, type 1.5 and press ENTER. For Right Bound?, type 2.5 and press ENTER. For Guess?, type 2 and press ENTER. These bounds isolate the first crossing in this example.
1.5ENTER2.5ENTER2ENTERWhat you should see: A zero near X = 2, with Y = 0. Numerical output may be approximate.
5. Find and check the other root
Repeat 2nd → TRACE → 2:zero with left bound 2.5, right bound 3.5 and guess 3, pressing ENTER after each value. Substitute both results into the original equation. Other equations need different windows and bounds.
2ndTRACE2:zeroWhat you should see: The second zero is near X = 3. Both 2 and 3 satisfy X² − 5X + 6 = 0.
Why this works
The zero tool searches for one root in a chosen interval; it does not list every solution. Here, (X − 2)(X − 3) = 0 confirms the two roots. Calculator results are numerical approximations.
Something looks different?
ERR:NO SIGN CHANGE
For a crossing, choose closer bounds on opposite sides of the x-axis and a guess inside them. A repeated root such as X² = 0 can only touch the axis, so this error is not proof that no real root exists.
Only one root was found
Run zero again around another visible crossing. Check other intervals or a wider view when appropriate; one search does not enumerate all roots.
Try a free worked tutorial
These optional tutorials are a starting point. You can ask about any calculator task in the question box above.
Free guides · No sign-in required
These three guides cover function graphing, viewing windows and graph zeros. Key names are shown as printed on the calculator; screen layouts can vary with software versions.
Before you start: function mode
Press MODE. Use the arrow keys to select FUNC (Func on some versions) and press ENTER. Press 2nd, then MODE (QUIT) to leave the menu. These examples use ordinary function graphing. Preserve any work you need before changing entries or settings.
Draw a function
0 of 4 steps marked done
- 1
Prepare the function editor
Y=ENTEROpen Y=. Preserve any entries you need and use an unused Y line; this example uses Y₁. To turn unrelated functions off, move to their highlighted = signs and press ENTER. If any Plot labels at the top are highlighted, move to them and press ENTER to turn them off.
What you should see
An available Y line is enabled. Unrelated functions and statistical plots are off.
- 2
Enter the function
X,T,θ,nx²−4On your chosen line, enter X² − 4. Use X,T,θ,n for X and the subtraction key − between X² and 4. Check that the = sign on this line is selected.
What you should see
Your enabled Y line contains X² − 4.
- 3
Show the graph
ZOOM6:ZStandardPress ZOOM and choose 6:ZStandard. This sets both axes from −10 to 10 and draws the graph.
What you should see
An upward-opening parabola, with its lowest point at (0, −4).
- 4
Read a point
TRACE←→Press TRACE and move left or right along the curve. The displayed X and Y coordinates describe the point under the cursor. Cursor values may be approximate.
What you should see
At X = 0, Y = −4. The curve crosses the x-axis near X = −2 and X = 2.
Fix a missing graph
0 of 4 steps marked done
- 1
Enter a graph outside the standard view
Y=X,T,θ,nx²+20In Y=, use an unused enabled Y line to enter X² + 20. Preserve existing entries and turn unrelated functions and Plot labels off. In the standard −10 to 10 view, this curve is above the visible area.
What you should see
The expression is entered. A blank standard view is possible because the lowest Y value is 20.
- 2
Set the viewing rectangle
WINDOW(-)↓Press WINDOW. Set Xmin = −5, Xmax = 5, Xscl = 1, Ymin = −5, Ymax = 30 and Yscl = 5. Use the (-) negative-number key for −5. Leave Xres unchanged.
What you should see
Each minimum is smaller than its maximum. Xscl and Yscl are positive.
- 3
Draw again
GRAPHPress GRAPH to draw with the new window. You do not need to change the function.
What you should see
The vertex at (0, 20) and part of the curve around it are visible.
- 4
Know how to restore the standard view
ZOOM6:ZStandardZOOM → 6:ZStandard restores both axes to −10 through 10. Try it if you want to compare views; X² + 20 can disappear again because the standard window does not suit this example.
What you should see
The viewing window changes; your function stays X² + 20.
Solve an equation with its graph
0 of 5 steps marked done
- 1
Graph the expression that should equal zero
Y=X,T,θ,nIn Y=, use an unused enabled line to enter X² − 5X + 6. Preserve your existing work and turn unrelated functions and Plot labels off. For an equation L = R, graph L − R instead.
What you should see
Your enabled Y line contains X² − 5X + 6.
- 2
Choose a useful window
WINDOWGRAPHIn WINDOW, set Xmin = 0, Xmax = 5, Xscl = 1, Ymin = −1, Ymax = 7 and Yscl = 1. Use (-) to enter −1. Press GRAPH.
What you should see
A parabola crosses the x-axis near X = 2 and X = 3.
- 3
Open the zero tool
2ndTRACE2:zeroPress 2nd, then TRACE to open CALC. Choose 2:zero. If more than one function is enabled, use the up/down arrows to select the intended curve.
What you should see
The calculator asks for Left Bound?.
- 4
Find the first root
1.5ENTER2.5ENTER2ENTERFor Left Bound?, type 1.5 and press ENTER. For Right Bound?, type 2.5 and press ENTER. For Guess?, type 2 and press ENTER. These bounds isolate the first crossing in this example.
What you should see
A zero near X = 2, with Y = 0. Numerical output may be approximate.
- 5
Find and check the other root
2ndTRACE2:zeroRepeat 2nd → TRACE → 2:zero with left bound 2.5, right bound 3.5 and guess 3, pressing ENTER after each value. Substitute both results into the original equation. Other equations need different windows and bounds.
What you should see
The second zero is near X = 3. Both 2 and 3 satisfy X² − 5X + 6 = 0.
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