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Online graphing calculator

Type a function such as x^2 - 2 or sin(x) and the graph appears instantly – with roots and turning points listed in the table.

Allowed: + − * / ^, brackets, 2x instead of 2*x, pi, e, sin, cos, tan, sqrt, abs, exp, ln, log, root(x, 3) and more.
Your inputs are saved in this browser only.

-5-4-3-2-112345-4-3-2-11234x^2 - 2sin(x)

Drag the graph to pan; Ctrl + mouse wheel or +/− to zoom.

Result

Roots and extrema in the visible range
FunctionTypexy
f1(x) = x^2 - 2Root-1.414210
f1(x) = x^2 - 2Minimum0-2
f1(x) = x^2 - 2Root1.414210
f2(x) = sin(x)Maximum-4.712391
f2(x) = sin(x)Root-3.141590
f2(x) = sin(x)Minimum-1.5708-1
f2(x) = sin(x)Root00
f2(x) = sin(x)Maximum1.57081
f2(x) = sin(x)Root3.141590
f2(x) = sin(x)Minimum4.71239-1

How it is calculated

What does the parabola look like, where does the sine cross the axis, where is the maximum? This graphing calculator plots up to three functions on one set of axes and finds the key points too – handy for homework, checking answers and exploring.

How it works

  1. Type a function such as x^3 - 3x, 2sin(x) or sqrt(x). The multiplication sign may be left out.
  2. Set the range with “x from/to” and “y from/to”, drag the graph or zoom with +/−.
  3. The table lists roots, maxima and minima in the visible x range; they are marked as circles on the graph.
  4. Use “Share” to pass the view on as a link, or save the graph as PNG or SVG.

How it is calculated

A custom parser turns the expression into a calculation tree – no code is executed. For roots, the range is sampled in 4,000 steps and each sign change is narrowed down by bisection (NIST DLMF §3.8); poles such as in tan(x) or 1/x are filtered out. Extrema are found from sign changes of the slope (central differences, DLMF §3.4) and refined with golden-section search. Touching roots such as in x² are found as extrema with y = 0.

Honest limits

Results are numerical, not exact formulas: √2 appears as 1.41421. Very close roots or rapidly oscillating functions may be missed – zoom in to help. Only functions of x; no parametric curves, inequalities or 3D. Angles are in radians.

Frequently asked questions

How do I enter powers and roots?

Powers with ^ (x^2, x^(1/3)), square root with sqrt(x), n-th root with root(x, n) – for example root(x, 3) for the cube root.

Does it use degrees or radians?

Radians, as is usual for function graphs. For degrees write sin(x*pi/180).

How accurate are roots and extrema?

They are shown numerically to about six significant digits. For exact values (e.g. √2) work it out by hand or with a computer algebra system.

Why is a root missing?

It is probably outside the x range or very close to another root. Widen the range or zoom in on that spot.

Sources and legal basis

As of:

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