How to Graph on a TI-84 Calculator

Introduction

Graphing is one of the most useful TI-84 skills because it helps you see equations instead of only calculating values. A graph can show roots, intercepts, turning points, increasing intervals, and behavior that may be hard to notice from the equation alone.

You can use the online TI-84 calculator on this site to practice basic graphing before using a physical calculator in class. The goal is not only to press GRAPH, but to understand the full workflow: enter the function, choose a good window, inspect the curve, and connect the graph back to the algebra.

Before you graph

Check the equation first. Make sure you know which variable is being graphed and whether the expression is written as `y =`. Most TI-84 graphing starts from the Y= menu, so equations like `x^2 - 4x + 3 = 0` are usually entered as `Y1 = x^2 - 4x + 3`.

If the expression uses fractions, parentheses, square roots, or negative numbers, enter them carefully. Parentheses are especially important for expressions such as `(x + 2)/(x - 3)` or `sqrt(x + 5)`.

Step-by-step instructions

1. Press the Y= key.
2. Clear old functions in Y1, Y2, or other lines if they are not part of the problem.
3. Type the function into Y1. For example, enter `x^2 - 4`.
4. Press GRAPH to draw the function.
5. If the graph looks empty, press ZOOM and choose a standard window.
6. Use TRACE to move along the curve and inspect x and y values.
7. Use WINDOW when you need custom x-min, x-max, y-min, and y-max values.
8. If the graph still looks wrong, return to Y= and check your input.

Practical example

To graph `y = x^2 - 4`, enter `x^2 - 4` in Y1. The graph should cross the x-axis at `-2` and `2`. This matches the factored form `(x - 2)(x + 2)`, so the graph confirms the algebra.

For a linear example, enter `Y1 = 2x + 3`. The graph should rise from left to right and cross the y-axis at `3`. If you use TRACE, you should see that increasing x by 1 increases y by 2. This connects the graph to the slope-intercept form `y = mx + b`.

How to choose a good graph window

Many graphing problems are not calculator errors. They are window errors. If the curve is off screen, too flat, or too zoomed in, the TI-84 may show an empty-looking graph.

A standard window is a good first step for basic algebra. For larger numbers, adjust WINDOW manually. A quadratic like `y = x^2 - 50` needs a y-range that includes negative values and a high enough positive range. A trig function may need an x-range that matches radians or degrees.

Use these checks:

• If the graph is blank, widen the x-range and y-range.
• If the curve is very steep, zoom out.
• If you only see a tiny piece of the graph, reduce the zoom level.
• If intercepts matter, make sure the x-axis and y-axis are visible.

When to use TRACE, TABLE, and ZOOM

GRAPH shows the picture, but the other tools help you interpret it. TRACE is useful when you want approximate coordinates on the curve. TABLE is useful when you want exact input-output pairs for selected x-values. ZOOM is useful when the window does not show the important part of the function.

For homework, you may use all three together: graph first, trace important points, then open the table to compare values. This is especially helpful for quadratics, intersections, and word problems where you need to explain what a point means.

Common mistakes

• Forgetting to clear an old function in Y2 or Y3.
• Typing a minus sign instead of the negative key when entering negative values.
• Using a window that is too zoomed in or too zoomed out.
• Missing parentheses around grouped expressions.
• Entering `y =` into the expression line instead of only the right side.
• Forgetting whether the calculator is in degree or radian mode for trig graphs.

FAQ

Why is my graph blank?

Your graph may be outside the current window. Try a standard zoom or adjust WINDOW values.

Can I graph more than one function?

Yes. Enter another function in Y2, Y3, or another open line.

How do I find an x-intercept from a graph?

Graph the function, then inspect where the curve crosses the x-axis. On a physical TI-84, you can use the zero feature from the CALC menu. For practice, you can also use the table and look for sign changes around the root.

Why does my graph look different from my teacher's graph?

The most common reason is a different window. Compare Xmin, Xmax, Ymin, and Ymax. Also check whether old functions are still turned on.

Where should I learn the full TI-84 workflow?

Start with the complete TI-84 guide, then return to the calculator on the homepage to practice.

Try the calculator on this site when you want quick browser practice without opening a separate emulator.