A Free Graphing Calculator in Your Browser: Plot Functions, Roots and Intersections
A quadratic on paper is a string of symbols. Plotted, it's a curve that crosses the x-axis in two places, and suddenly "roots" make sense. Graphing calculator draws functions of x, lets you pinch and drag to explore, and lists the roots and crossings it finds in the window you're looking at.
Steps
- Enter one or more functions of x, one per line, such as
x^2 - 5x + 6orsin(x). - Drag to pan, pinch or scroll to zoom, or set the window yourself.
- Read the roots and the crossing points inside the visible window.
What you can plot
Polynomials, roots, absolute value, and the usual functions: sin, cos, tan and their inverses, sinh, cosh, tanh, ln, log, exp and sqrt. Implied multiplication works, so 2x and (x-2)(x-3) are fine. Powers use ^.
Angles are in radians until you switch to degrees. In degrees, sin(90) is 1. A whole-number power of a negative value keeps its sign, so (-2)^3 is −8.
Up to eight curves are drawn at once, and the page lists where each pair crosses.
Roots and crossings depend on the window
Roots and intersections are found inside the window on screen. If you expect a root and it's missing, widen the x minimum and maximum, or zoom out, and it appears once it's in view. That's also a good habit for exams: always check the graph's full shape before trusting a list of roots.
Things to try
Quadratics. Plot x^2 - 5x + 6. Roots at 2 and 3, matching the factorised form (x-2)(x-3). Add x^2 - 5x + 7 and notice it never touches the axis: no real roots, discriminant negative.
Solving equations graphically. To solve 2^x = x + 2, plot both sides as separate lines and read the crossings.
Transformations. Plot sin(x), 2sin(x), sin(2x) and sin(x) + 1 together and watch amplitude, period and vertical shift change.
Growth comparisons. x^2, 2^x and ln(x): which wins as x grows? Zoom out to see.
Absolute value. abs(x - 3) - 2 makes a V; find its vertex and roots.
Tips for students
- Use it to check, not replace, your algebra. Solve by hand, then plot to confirm.
- Mind radians vs degrees, especially for trigonometry homework done in degrees.
- Zoom in on near-misses. Two curves that look like they touch might just come close; zooming tells you.
- Write brackets explicitly for fractions:
1/(x+1), not1/x+1.
On a phone
Put two fingers on the graph and pinch to zoom; drag with one finger to pan. The Zoom in and Zoom out buttons work too, and on a computer you can scroll with the pointer over the graph.
For straightforward calculation, pair this with the Scientific calculator.
Reading a graph like an examiner
When you plot a function, look for five things: where it crosses the x-axis (roots), where it crosses the y-axis (set x to 0), turning points, behaviour as x gets very large or very negative, and any breaks or asymptotes, as in 1/x. Sketch questions in exams usually award marks for exactly these features. Plot your function, note each one, and you have a checklist for drawing it by hand.
Privacy
According to the page, everything runs in the page and stays on your device. The page shows Google ads, as across the site.
FAQ
How do I zoom on a phone? Pinch with two fingers, or use the zoom buttons.
Which angle unit does sin use? Radians by default; switch to degrees with the control.
Why is a root missing? It's outside the visible window. Zoom out or widen the range.
Can I plot more than one curve? Yes, up to eight, one per line.
See your equations with Graphing calculator.
— Alok Kumar Singh