How to Graph on a TI-84 Calculator — Step-by-Step Guide

By Miqdad Qaisrani | Updated October 13, 2026

Graphing is the centrepiece of everything the TI-84 does. For many students, the moment they first see a function appear as a smooth curve on the screen is the moment math starts to click. This page is a complete walkthrough of the graphing workflow — from typing in a simple Y= equation all the way to finding intersection points between two curves. It covers what you can do with the Calc84 graphing engine and explains how the online graphing experience compares with button presses on a physical device.

Entering and plotting Y= functions

The Y= editor is where every graph begins. Press Y= (the top-left key on the physical TI-84, or the equivalent onscreen button on the online calculator) and you will see a list of function slots labelled Y₁ through Y₀. Up to ten functions can be active at once.

When you type a function, use the X,T,θ,n key for the variable. The calculator treats X as the independent variable for rectangular (Y=) mode. For example, entering Y₁ = X² - 4 and pressing GRAPH produces a parabola opening upward, with its vertex at (0, -4) and intercepts at x = -2 and x = 2. The screen auto-scales based on the current WINDOW settings, which default to Xmin = -10, Xmax = 10, Ymin = -10, Ymax = 10 (the ZStandard zoom level).

Functions can include any of the operations available on the keypad: addition, subtraction, multiplication, division, exponents (using the ^ key), trigonometric functions (SIN, COS, TAN), logarithms (LOG, LN), and the full MATH menu including roots, absolute value, and numeric operations. All of these operations are available in the online TI-84 calculator.

Polar and parametric graphing modes

Beyond the familiar Y= rectangular mode, the TI-84 supports three additional graphing modes accessed through the MODE key:

• Polar mode (r =): Select Pol in the MODE menu to graph equations in terms of radius r and angle θ. For example, r = 2sin(3θ) produces a three-petaled rose curve. The WINDOW settings change — you now set θmin, θmax, and θstep (in radians or degrees, depending on MODE). Polar mode is widely used in precalculus and physics for conic sections and orbital paths.
• Parametric mode (x(t), y(t)): Select Par to define both x and y as functions of a third parameter t. For example, x(t) = 5cos(t) and y(t) = 3sin(t) with t from 0 to 2π draws an ellipse. This mode is critical for calculus when tracing motion along a path, and for plotting curves that are not single-valued functions (like circles or Lissajous figures).
• Sequence mode: Select Seq to plot recursively defined sequences, useful for discrete math and exploring limits.

The online graphing calculator supports function, polar, and parametric modes. Switch modes with the Graphing Mode selector (Func, Par, or Pol), enter your equations in the Y= editor (which adapts to the selected mode), and press GRAPH. If you are working on a free online TI-84 calculator, you can switch between modes without clearing existing equations — something that is especially helpful when comparing rectangular and parametric representations of the same curve.

Inequality graphing: shading above or below

Inequality graphing is a built-in TI-84 feature that shades the region above or below a curve. In the Y= editor, move the cursor to the left of the equals sign and press ENTER repeatedly to cycle through the inequality symbols: = (equal), > (greater than), < (less than), ≥ (greater than or equal), and ≤ (less than or equal).

For instance, setting Y₁ to ≥ X + 1 and Y₂ to ≤ 5 - X² shades the overlapping region that satisfies both inequalities — a visual solution to a system of inequalities. This is especially useful for linear programming problems in algebra and for visualising feasible regions. The graph uses shaded patterns that are easy to read, and pressing TRACE lets you examine boundary points.

Shading in the Calc84 graphing engine is a rendering style applied to a plotted curve — the area above or below the curve you enter is filled in — rather than the full inequality-symbol entry described above, which is a TI-84 hardware feature.

Using TRACE and the CALC menu to analyze graphs

Graphing a function is just the start. The real power comes from the analysis tools:

• TRACE mode: Press TRACE after graphing to move a cursor along the curve. The x and y coordinates of each point display at the bottom of the screen. Use the left and right arrow keys to step along the curve. On the online version, you can also click directly on the graph to jump to a point.
• CALC menu (2nd + TRACE): This is the powerhouse. Options include:
  • 1: value — evaluate Y at a specific X you type in.
  • 2: zero — find roots (x-intercepts). The calculator asks for a left bound, right bound, and guess, then computes the x-value where y = 0.
  • 3: minimum / 4: maximum — locate local extrema within an interval you specify.
  • 5: intersect — find where two curves cross. After selecting the two curves and a guess, the TI-84 returns (x, y) coordinates of the intersection point.
  • 6: dy/dx — compute the derivative (slope) at a point.
  • 7: ∫f(x)dx — compute the definite integral between two x-values, shading the area under the curve.

These CALC tools are available on the online graphing calculator too. The intersection tool (option 5) is particularly efficient — it solves the system of equations Y₁ = Y₂ numerically without requiring algebraic manipulation.

ZOOM options: framing your graph perfectly

The ZOOM key opens a menu of preset and custom zoom options that control the WINDOW ranges:

• ZStandard (6): Resets X to [-10, 10] and Y to [-10, 10] with Xscl = Yscl = 1. This is the default view and a good starting point for most functions.
• ZBox (1): Lets you draw a rectangle with the cursor to zoom into a specific region. Move the cursor to one corner, press ENTER, move to the opposite corner, and press ENTER again.
• ZDecimal (4): Sets X to [-6.6, 6.6] and Y to [-4.1, 4.1], with ΔX = 0.1 and ΔY = 0.1. This is handy for tracing at clean 0.1 increments.
• ZSquare (5): Adjusts the Y range so that circles appear as actual circles (equal scaling on both axes). Useful for geometry problems.
• ZTrig (7): Presets the window for trigonometric functions with X from -2π to 2π in radian mode.

The online calculator makes zooming even faster — you can click and drag to pan, scroll to zoom, or use the keyboard shortcuts. On a physical TI-84, zooming requires navigating menus with arrow keys, which is precise but slower. The browser-based version on Calc84 gives you both approaches, so you can use whichever you find more natural.

Online graphing workflow vs. physical TI-84 button presses

The online graphing experience maps directly to the hardware button layout, but with a few meaningful differences:

The key difference is speed. On the physical calculator, adjusting the window for a clear view of your graph can involve several rounds of WINDOW edits. Online, you can drag and zoom intuitively. This makes the online version excellent for exploration — you can try different window ranges quickly and see the results instantly.

Practice problem: graph y = sin(x)cos(2x)

Here is a concrete example to try right now. Open the online TI-84 calculator and follow these steps:

1. Press MODE and make sure you are in Radian mode (not Degree). Trig functions behave more naturally in radians.
2. Press Y= and enter sin(X)*cos(2X) for Y₁. Use the X,T,θ,n key for X.
3. Press ZOOM, then select 7: ZTrig. This sets the window to X: [-2π, 2π] and Y: [-4, 4], which is perfect for trig functions.
4. Press GRAPH. You should see a wave pattern with amplitude that varies — the cos(2X) factor modulates the sin(X) wave, producing a distinctive envelope shape. In this window the curve reaches its highest value of y = 1 at x = -π/2 and x = 3π/2, and its lowest value of y = -1 at x = π/2. It also passes through zero several times, including at x = 0, ±π, and ±2π.
5. Press TRACE and move along the curve. Note that the y-values oscillate between approximately -1 and 1, since both sin(X) and cos(2X) are bounded by [-1, 1] and their product cannot exceed those bounds.
6. Press 2nd + TRACE (CALC), select 4: maximum. Set a left bound near x = 0, a right bound near x = 1, and a guess near x = 0.4 — the curve has a small local maximum between the zeros at x = 0 and x = π. The calculator should return x ≈ 0.42 with y ≈ 0.27.

This one function demonstrates TRACE, ZTrig, and the CALC maximum-finding tool — the three graphing skills you will use most often.

Frequently asked graphing questions

For additional graphing techniques, see Khan Academy's graphing tutorial and TI's official 10-minute graphing guide.

Graphing on the TI-84 is a skill that gets faster with practice. The free online TI-84 graphing calculator gives you a risk-free way to explore — you can try things, make mistakes, zoom in and out, and discover how functions behave without worrying about batteries or carrying a calculator. Open the main calculator page and start plotting.

Page last updated: October 13, 2026

Miqdad Qaisrani

Creator of Calc84

Miqdad is a full-stack engineer and cybersecurity student specializing in educational technology (EdTech). He built Calc84’s online graphing calculator to give students free graphing, TRACE, ZOOM, and CALC tools in the browser.

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