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The display shows the graph of y = (x-a)(x-b)(x-c) , where a, b and c are constants. Graphs like these are called cubic graphs.
Investigate the effect of changing a, b and c.
Make sure that you are clear about these aspects of a cubic graph:
  • its basic shape
  • its symmetry
  • the number of places where the curve crosses the x-axis

Software/Applets used on this page

This page uses JSXGraph

JSXGraph is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. It is implemented completely in JavaScript, does not rely on any other library. It uses SVG and VML and is fully HTML5 compliant.



A mathematical expression of the 3rd degree; having a x³ term but no higher one.


A rule that connects one value in one set with one and only one value in another set.


A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.


To mark a point on a graph accurately by using its coordinates.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA GCSE (9-1) Foundation (UK)A: GraphsA12: Sketching Graphs of FunctionsGraphs of Cubics-
CBSE IX (India)AlgebraPolynomialsConstant, linear, quadratic and cubic-
CIE IGCSE (9-1) Maths (0626 UK)2 Algebra and GraphsB2.10 Further GraphingGraphs of Cubics-
Edexcel GCSE (9-1) Foundation (UK)A: GraphsA12: Sketching Graphs of FunctionsGraphs of Cubics-
GCSE Higher (UK)AlgebraGraphsCubic curves-
OCR GCSE (9-1) Foundation (UK)7: Graphs of Equations and Functions7.01c: Polynomials and Exponential FunctionsGraphs of Cubics-
Universal (all site questions)GGraphsCubic curves-