Graphing calculator

What you can type

• Functions: y = x^2 - 3x, sin2x, e^-x, |x - 1|, sqrt(x), ln x, log_2(x)
• Your own functions: f(x) = x^3 - 3x, then f(x - 2) + 3 or f'(x)
• Sliders: any letter you have not defined, like a in y = a(x - h)^2 + k, offers a slider; ▶ animates it
• Points and lists: (2, 3), n = [1...10], (n, 2n + 1). Drag a point like (h, k) to move its sliders; a label such as (${h}, ${k}) shows its values
• Piecewise and restrictions: {x < 0: -x, x^2}, y = sqrt(x) {0 <= x <= 4}
• Calculator: int_0^2 x^2 dx, sum_(n=1)^(10) n^2, mean(y_1), nCr(5, 2)
• Started in Desmos? Import from Desmos brings in copied expressions, sliders and table cells, and tells you anything it couldn't bring in.

Straight lines and quadratics

Type the equation as it is written in the question:

• y = m x + c gives sliders for m and c: drag m to change the gradient and c to move the y-intercept
• y = 3 - 2x: tap the line to see where it crosses each axis
• y = x^2 - 2x - 3: tap the curve for its roots, its turning point and the y-intercept
• Solve graphically: add y = x + 1 to the quadratic, and the intersections are the solutions of x² − 2x − 3 = x + 1
• Regions: y > 2x - 1 and y <= 4 - x shade the sides of each line

In the exam you draw the graph from a table of values. Select a curve and tap table of values to check your table, then check the points you plotted.

Practise it: 4MA1 straight-line graphs · 4MA1 quadratic and cubic graphs · 0580 gradient

Reading the graph

• Tap a curve to select it: grey dots mark its roots, turning points, y-intercept and intersections with other curves. Tap a dot for its coordinates, or drag along the curve to trace it.
• Drag to move; pinch, scroll or use + and − to zoom; ⌂ resets, ⤢ fits your data, □ makes the axes square.
• Keyboard: focus the graph, then arrow keys move and + / − zoom. More → Data table lists the values and points of interest.
• Undo and Redo (the arrows by More, or Ctrl+Z and Ctrl+Shift+Z; ⌘ on a Mac) take back changes, even loading an example over your graph.
• In More, Share link puts the whole graph in the link (nothing is uploaded, so pictures you add are not included); Export downloads a PNG or an SVG, with your residual plots if you want them. Your graph, with its pictures, is also kept in this browser.
• On a phone the graph stays at the top while you scroll your lines, and the maths keypad (More → Maths keypad) gives you ^, √, π, θ, x₁ and ~ without switching keyboards. Select a curve and tap table of values for a table.
• Save keeps it in My graphs with a free account (up to 200 graphs, and up to 5 pictures per graph), to open, rename or delete on any device.
• Pictures are made smaller in your browser before they are used (at most 1600 pixels across), which also removes the photo's hidden details such as its location.

Practising for a calculator paper? Edexcel 4MA1 allows a calculator in every paper. Cambridge 0580 allows none in Papers 1 and 2, and a scientific calculator in Papers 3 and 4. See the calculator guides. This grapher is our own tool; the ~ syntax follows the convention many graphing tools use.

Practise with it

• Straight-line graphs (4MA1) · equation of a straight line (0580)
• Gradient (0580) · parallel and perpendicular lines (0580)
• Quadratic and cubic graphs (4MA1) · graphs of functions (0580)
• Graph transformations (4MA1) · trigonometric graphs (4MA1)
• Inequalities on graphs (4MA1) · real-life graphs (4MA1)

Draw it by hand first, then check it here.