How to calculate graphing
Graph of y = f(x) sampled at 400 points across [x from, x to] Roots: sign change of f(x), refined by bisection Intersections: roots of f(x) − g(x)
Worked example. y₁ at x = 3: 5.
Example inputs — y₁ = f(x): x^2 - 4; y₂ = g(x) (optional): 2x + 1; x from: -10; x to: 10; Evaluate y₁ at x =: 3; Angle unit: Radians. Starting values are illustrative.
From George Guju, founder of Calculyn · Educational calculator guidance, not professional advice.
How it works
Type a function of x and the graph updates instantly. You can write 2x instead of 2*x, use ^ for powers, and use sqrt, cbrt, abs, sin, cos, tan, asin, acos, atan, log (base 10), ln, exp, pi and e. Add a second function to see where the two lines cross. Roots, intersections and the highest and lowest points are found numerically within the x range you choose — widen or narrow the range to zoom.
Assumptions & limitations
- Results are rounded for display.
Formula and assumptions reviewed October 2026 by the Calculyn team. How we build our calculators
Frequently asked questions
How do I graph a parabola?
Type it in the form a x^2 + b x + c, for example x^2 - 4 or -2x^2 + 3x + 1. The lowest (or highest) point shown is the vertex when it's inside your range.
How do I find where two graphs intersect?
Enter one function in y₁ and the other in y₂. The intersections are listed below the answer, and you can see them on the graph.
Why are trig graphs in radians?
Graphs of sin(x) and cos(x) are usually drawn in radians, where one full wave spans 2π ≈ 6.28. Switch to degrees under More options if you prefer.
Can it graph things like 1/x?
Yes. Points where the function is undefined (like x = 0 for 1/x) are skipped, so the graph shows a break there.