Online graphing calculator

A number next to x means multiply, so 3x is 3 × x. You can type "y =" at the start or leave it out. Trig graphs use radians here, so sin(x) repeats every 2π (about 6.28) along the x-axis.

Graphs let you solve equations you can't easily solve by algebra. To solve f(x) = 0, read off the roots, where the graph crosses the x-axis. To solve f(x) = g(x), graph both and read off where they meet. For example, graphing y = x² − 2x − 3 and y = 2x + 1 shows they meet where x² − 2x − 3 = 2x + 1. This is exactly the method GCSE and IGCSE questions ask for when they say "use the graph to solve...".

For y = x² − 2x − 3:

• The roots are x = −1 and x = 3 (it factorises to (x + 1)(x − 3)).
• The y-intercept is −3, the number on the end.
• The turning point is halfway between the roots, at x = 1, so it's (1, −4).
• It's a U shape because the x² term is positive; a negative x² term gives an upside-down curve.

Practise this with our quadratic graphs questions.

In y = mx + c, m is the gradient and c is where the line crosses the y-axis. Graph y = 2x + 1 and y = 2x − 3: they're parallel because they have the same gradient. Graph y = 2x + 1 and y = −x/2 + 1: they cross at right angles, because the gradients multiply to −1. See our straight line graphs questions for practice.

Roots and intersections are found numerically (the calculator narrows in on each one), and shown to 5 significant figures, which is more than enough for checking homework. They're listed only for the part of the graph you can see, so zoom out if you expect more. Graphs with sudden jumps, like 1/x or tan(x), are drawn with gaps at the jump rather than a misleading vertical line.