Graphing Calculator
Plot up to 6 functions at once, drag sliders to explore them, and read off roots, intercepts, extrema and intersections instantly. Free, no sign-up, and it runs entirely in your browser.
Table of values
How to use the Graphing Calculator
- Type a function in the first row, for example x^2 – 4 or sin(x). The graph draws as you type.
- Press + Add expression to plot up to 6 functions together. Each one gets its own colour.
- Use a letter like a in an expression (try a*x + b) and a slider appears automatically. Drag it to watch the graph change.
- Drag the graph to pan, scroll or pinch to zoom, and double-click to reset. Roots, intercepts and extrema for the visible area are listed under each expression.
- Tap Table for a table of values, or Export PNG to save the graph as an image for your homework or slides.
What is a graphing calculator?
A graphing calculator draws the picture of an equation. Instead of only giving you a number, it shows you the whole relationship between x and y as a curve on a coordinate grid. That picture makes behaviour visible at a glance: where a function rises and falls, where it crosses the axes, how steep it is, and whether two functions ever meet. Teachers use graphs to connect algebra to geometry, and engineers use them to sanity-check formulas before trusting the numbers.
This online version covers the features students actually need from a handheld graphing calculator: multiple functions in different colours, movable sliders for parameters, automatic roots and turning points, a table of values, and an exportable picture, all without installing anything.
How to read a graph
Intercepts: where the curve crosses the axes
The y-intercept is the point where the curve crosses the y-axis. It happens when x = 0, so it is simply the value f(0). The x-intercepts are where the curve crosses the x-axis, where y = 0. Both are listed under each expression above whenever they fall inside the visible area.
Roots (zeros) of a function
The x-intercepts of a graph are also called the roots or zeros of the function, because they are the solutions of the equation f(x) = 0. For example, the roots of x² − 4 are x = −2 and x = 2, exactly where its parabola crosses the x-axis. Finding roots on a graph is often the fastest way to check an algebraic solution.
Slope, maxima and minima
The steepness of a curve at a point is its slope. Where the slope changes from positive to negative the curve has a local maximum; where it changes from negative to positive it has a local minimum. These turning points (together called extrema) are detected automatically and shown under the expression, for example “min ≈ (0, −4)” for the parabola y = x² − 4.
Common function families
Most graphs you will ever plot belong to a small set of families. Type each example into the calculator and compare its shape with the description.
| Family | Try this | Shape |
|---|---|---|
| Linear | 2x + 1 | A straight line; the slope and intercept are easy to read off. |
| Quadratic | x^2 – 4 | A parabola (U shape) with one minimum or maximum. |
| Cubic | x^3 – 3x | An S-shaped curve with a local max and a local min. |
| Trigonometric | sin(x) | A smooth repeating wave between −1 and 1. |
| Exponential | 2^x | Slow growth that quickly becomes very steep. |
| Logarithmic | ln(x) | Fast then slow growth; only exists for x > 0. |
| Rational | 1/x | Two separate branches with a vertical asymptote at x = 0. |
Worked example: plotting y = x² − 4
Type x^2 – 4 into the first row (it is loaded as the default example). Before looking at the answer, predict the picture: the x² term makes a parabola opening upwards, and the −4 shifts it down by 4.
Now check the facts under the expression. The y-intercept is (0, −4), because f(0) = 0² − 4 = −4. That same point is the minimum, since a parabola’s vertex sits on its axis of symmetry, x = 0. The roots solve x² − 4 = 0, so x² = 4 and x = 2 or x = −2, matching the two x-intercepts on the graph. Finally, add sin(x) in a second row: the intersections box reports where the parabola and the wave cross, something that is painful to solve purely by algebra.
Common mistakes
- Missing parentheses. sin(x + π) and sin(x) + π are completely different graphs. When in doubt, add brackets.
- Confusing log and ln. Here log means base 10 and ln is the natural logarithm (base e), the same convention as most scientific calculators.
- Expecting the line to join across gaps. Functions like 1/x, tan(x) and sqrt(x) have asymptotes or regions where they do not exist. The calculator deliberately breaks the line there instead of drawing a false connection.
- Losing the curve. After zooming far in or out, double-click the graph (or press Reset view) to return to the standard window.
- Forgetting trig uses radians. sin(x) completes one full wave every 2π units of x, not every 360.
Frequently asked questions
Is this graphing calculator free?
Yes. It is completely free to use, with no sign-up and no download. Everything runs in your browser, so your expressions are never sent to a server.
What functions can I plot?
You can plot polynomials, trigonometric functions (sin, cos, tan and their inverses), logarithms (ln and log), square roots, absolute values and exponentials. Type things like x^2 – 4, 2sin(x) or sqrt(x + 3), and use ^ for powers and π for pi.
How do I add a slider?
Use a single letter such as a, b, c or m in your expression, for example a*x + b. A slider for each letter appears under the expression automatically. Drag it and the graph updates instantly, which is perfect for seeing how a slope or intercept changes.
How do I find roots and intercepts?
They appear under each expression automatically. The calculator scans the part of the graph on screen, so zoom or pan if a root is off-screen. The y-intercept is where the curve crosses the y-axis (x = 0), and roots are where it crosses the x-axis (y = 0).
Can I use it on my phone or Chromebook?
Yes. The calculator is fully responsive and works with touch: drag to pan, pinch to zoom and tap a curve to trace it. It runs in any modern browser, including on school Chromebooks, with nothing to install.
How do I save my graph?
Press the PNG button above the graph to download an image of exactly what is on screen. You can then drop it into homework, slides or notes. To keep working on the same functions later, just leave the tab open or copy the expressions into your notes.