Graph Plotter — Online Graphing Calculator
Plot linear, quadratic and cubic graphs instantly. Enter your function, choose the graph type, and see the result on an interactive coordinate grid.
Tip: Adjust values and click Plot Graph to update the chart. Hover over the canvas to read coordinates.
What is a Graphing Calculator?
A graphing calculator (also called a graph plotter) is a tool that draws the visual representation of a mathematical function on a coordinate grid. Instead of calculating individual values by hand, you enter an equation — such as y = 2x + 3 — and the calculator automatically plots the corresponding curve or straight line across a range of x values.
Graphing calculators are essential for GCSE and A-level maths in the UK. They help students visualise abstract equations, identify roots and intercepts, and understand how changing coefficients affects the shape of a graph. Online graph plotters like this one, or tools like Desmos and GeoGebra, have made graphing accessible on any device without specialist hardware.
Types of Graphs You Can Plot
Linear Graphs — y = mx + c
A linear graph is the simplest type — it produces a perfectly straight line. The equation y = mx + c has two components:
- m (gradient): How steep the line is. A positive m slopes upward left to right; a negative m slopes downward. A gradient of 2 means the line rises 2 units for every 1 unit it moves right.
- c (y-intercept): Where the line crosses the y-axis (when x = 0).
Examples: y = x + 2 (gentle positive slope), y = -3x + 5 (steep negative slope), y = 0.5x (shallow slope through the origin).
Quadratic Graphs — y = ax² + bx + c
A quadratic graph produces a curved U-shape called a parabola. When a is positive, the parabola opens upward (like a U); when negative, it opens downward (like an n-shape). The vertex is the turning point — the lowest or highest point of the curve.
Key features to identify at GCSE: roots (where the curve crosses the x-axis), the vertex, the axis of symmetry, and the y-intercept. The discriminant (b² - 4ac) tells you how many real roots there are: positive = two roots, zero = one root (tangent to x-axis), negative = no real roots.
Cubic Graphs — y = ax³ + bx
A cubic graph produces a distinctive S-shaped curve with up to two turning points and up to three roots. When a is positive, the curve falls from bottom-left to top-right with an S twist. Cubic functions appear in GCSE Higher tier and A-level maths.
Other Common Graph Types
- Reciprocal graphs (y = k/x): produce hyperbola curves in opposite quadrants
- Exponential graphs (y = aˣ): rapid growth or decay curves
- Trigonometric graphs (y = sin x, y = cos x, y = tan x): wave patterns
- Circle graphs (x² + y² = r²): appear at GCSE Higher level
How to Plot y = mx + c Step by Step
- Identify m and c from the equation. For y = 3x - 2, m = 3 and c = -2.
- Plot the y-intercept: Mark the point (0, c) on the y-axis. Here, mark (0, -2).
- Use the gradient to find a second point: From (0, -2), move 1 unit right and m units up. With m = 3, move to (1, 1).
- Draw the line: Use a ruler to draw a straight line through both points and extend it across the grid.
- Check with a third point: Substitute x = 2 — gives y = 4. Mark (2, 4) and confirm it lies on your line.
Our graph plotter above automates this process — enter m and c, click Plot Graph, and it draws the line instantly with a table of values for reference.
Solving Equations by Graphing
Graphing is a powerful method for solving equations, especially when algebraic methods are complex. To solve by graphing:
- Rearrange the equation so one side equals y (or zero).
- Plot the resulting function.
- Find where the curve crosses the x-axis — these x-values are the solutions (roots).
Example: Solve x² - 2x - 3 = 0. Plot y = x² - 2x - 3. The parabola crosses the x-axis at x = -1 and x = 3, so the solutions are x = -1 and x = 3.
For simultaneous equations, plot both equations on the same graph. The point where the two lines or curves intersect gives the solution to both equations simultaneously.
Example: Solve y = 2x + 1 and y = -x + 7 simultaneously. The lines intersect at (2, 5), so x = 2, y = 5.
Graphing Calculators for GCSE Maths
The GCSE maths specification (all UK exam boards) includes graphical work throughout. Key graphing topics at GCSE include:
- Plotting and interpreting straight-line graphs (y = mx + c, x = a, y = b)
- Finding the gradient and y-intercept of a line
- Recognising and sketching quadratic, cubic, reciprocal and exponential graphs
- Solving quadratic equations graphically by reading roots from the x-axis
- Solving simultaneous equations graphically by finding intersection points
- Sketching and interpreting distance-time and velocity-time graphs
While graphing calculators are not permitted in GCSE exams, online plotters are invaluable for homework, coursework and revision. They allow you to check hand-drawn graphs instantly and build intuition about how changing coefficients affects the shape of a curve.
Frequently Asked Questions
How do you use a graphing calculator?
Enter your function using standard notation — for example y = 2x + 3 for a straight line or y = x² - 4 for a parabola. The calculator plots the graph on a coordinate grid. You can adjust the scale (window) to see different parts of the graph. For GCSE maths, identify intercepts (where the graph crosses the axes) and the gradient (steepness) of lines, or roots and vertex for quadratics.
What is the best graphing calculator app for GCSE?
Desmos is the most popular free online graphing calculator for GCSE students — it is intuitive, works on any device, and supports a wide range of functions. GeoGebra is another excellent free alternative. For physical calculators, the Casio fx-991EX is the top choice in UK schools. Our graph plotter is ideal for quick linear and quadratic plots without installing anything.
How do you plot y = mx + c?
Identify m (gradient) and c (y-intercept). Plot the y-intercept at (0, c), then use the gradient to find a second point by moving 1 unit right and m units up. Draw a straight line through the two points. For example, y = 2x + 1 has a y-intercept of 1 and rises 2 units per 1 unit across.
How do you solve equations by graphing?
Plot both sides of the equation as separate functions and find where they intersect. The x-coordinate at the intersection is the solution. For quadratic equations, plot y = ax² + bx + c and read off the x-values where the parabola crosses the x-axis — these are the roots of the equation.
What is the difference between a linear, quadratic and cubic graph?
A linear graph (y = mx + c) is a straight line. A quadratic graph (y = ax² + bx + c) is a U-shaped or inverted-U parabola. A cubic graph (y = ax³...) is an S-shaped curve. The highest power of x determines the type: power 1 = linear, power 2 = quadratic, power 3 = cubic.
Can I use a graphing calculator in my GCSE exam?
No — graphing calculators are not permitted in GCSE exams in England, Wales or Northern Ireland. Only scientific calculators (non-graphing) are allowed. However, online graphing tools are excellent for homework, revision and checking your work outside the exam room.