How to Use a Graphing Calculator

What a Graphing Calculator Does

A graphing calculator is a small computer for math. It draws graphs, solves equations, and works with numbers in tables. A normal scientific calculator gives you one answer at a time. A graphing calculator shows you the whole picture — the shape of a function, where it crosses zero, and where it goes up or down.

Most graphing calculators have the same main keys: Y= for typing a function, GRAPH for drawing it, WINDOW for setting the view, TRACE for reading values, and TABLE for lists. Learn these five keys and you can do most of your homework.

If you are new to this, start with a free online calculator. Our TI-84 style graphing calculator works in your browser and has the same keys and screens as the hand-held model.

Step 1: Open the Graph Screen

Turn the calculator on and press the Y= key, near the top left of the keypad. You will see a list that starts with Y1=, Y2=, and so on. This list is where functions live. Each line is one function. You can graph up to ten functions at once, but one is enough to start.

Before you type anything, clear old functions. Move the cursor to an old Y1= line and press CLEAR. Do the same for any other line that has a function. A clean list means no old graph will mix with your new one.

Next, look at the top of the screen. Each function has a small icon next to it. If the icon is dark, the function is on. Press the left arrow key to move to the icon, then press ENTER to switch it on or off. For now, keep only Y1 on.

Step 2: Type Your First Function

Let us graph a simple line first: y = 2x + 1. Move the cursor after Y1= and type 2, then the X,T,θ,n key (this key types X), then + 1. Press GRAPH. You will see a straight line that goes up from left to right.

Now try a curve. Press Y= again, clear Y1, and type X^2 with the X,T,θ,n key and the x² key. Press GRAPH. The screen shows a parabola — a U shape with its lowest point at zero.

A few typing tips help a lot. Use the ( and ) keys around fractions and powers, for example Y1=(X+2)^2 and not Y1=X+2^2. Use the (−) key for a negative number, not the minus key. If the calculator shows a syntax error, the problem is almost always a missing bracket.

Step 3: Set the Window So You Can See the Graph

Sometimes you press GRAPH and see nothing, or only a small part of a curve. This is a window problem, not a math problem. The window is the part of the graph the screen shows. Press the WINDOW key to see the settings.

The standard window is Xmin = −10, Xmax = 10, Ymin = −10, Ymax = 10. To get it fast, press ZOOM and choose 6: ZStandard. The calculator resets the window and draws the graph again.

For a closer look, use ZOOM and choose 2: Zoom In, then press ENTER near the point you want to see. For a wider view, choose 3: Zoom Out. You can also set the window by hand. If you graph y = x² − 100, set Ymin to −120 so the bottom of the parabola is visible.

To graph two functions at once, type one in Y1 and one in Y2, then press GRAPH. Both curves appear on the same screen. This is how you compare functions, or find where they cross.

Step 4: Read the Graph with Trace and Table

A graph is more than a picture. You can read exact values from it. Press TRACE after you graph a function. A small cursor appears on the curve. Use the left and right arrow keys to move it. The bottom of the screen shows the x and y values at the cursor. This is the fastest way to answer "what is y when x = 3?"

For a full list of values, press 2nd then GRAPH to open the table. It shows x values in one column and y values in the next. Change the step size in TBLSET (2nd, then WINDOW).

Step 5: Solve Problems on the Graph

The CALC menu does the hard work for you. Press 2nd then TRACE to open it. Here are the tools you will use most:

• 2: zero — finds where the graph crosses the x-axis. Pick a left bound, a right bound, and a guess, and it gives you the zero.
• 3: minimum and 4: maximum — find the lowest or highest point of a curve, for example the vertex of a parabola.
• 5: intersect — finds where two graphs cross. Graph both functions first, then choose this tool.
• 1: value — gives you y for any x you type.

Try it with y = x² − 4. Graph it, open CALC, and choose 2: zero. For the left zero, pick a left bound of x = −3, a right bound of x = −1, and a guess of x = −2. The calculator shows x = −2. Repeat for the right zero to get x = 2.

Common Mistakes and How to Fix Them

Every student hits the same few problems. Here are the fixes:

• Blank screen: press ZOOM, then 6 for ZStandard. The graph was outside the window.
• Syntax error: check your brackets. Count the open and close brackets in the function.
• Wrong graph shape: an old function is still on. Press Y=, clear every line except the one you want.
• Window too small: the graph looks like a flat line. Zoom out or set Ymin and Ymax by hand.
• Mode is wrong: if trig graphs look strange, check MODE. For most school work, the angle mode should be degrees, and the function mode should be Func, not Par or Pol.
• Stat plots on: if dots or lines appear that you did not graph, press Y=, move to the top, and turn off Plot1, Plot2, and Plot3.

Practice: Try These Three Graphs

Practice makes the keys feel natural. Try these three, one at a time, on our graphing calculator simulator or on a real calculator:

1. Graph y = x + 3. Use TRACE to find y when x = 5. (Answer: y = 8.)
2. Graph y = x² − 9. Use CALC zero to find both zeros. (Answers: x = −3 and x = 3.)
3. Graph y = 2x + 1 and y = −x + 4 together. Use CALC intersect to find where they cross. (Answer: x = 1, y = 3.)

Once you can do these three, you know the core of graphing. Next, try a 3D graph or a polar graph.

Frequently Asked Questions