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:

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.

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.

## Glossary

### cubic

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

### function

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

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### plot

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

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AQA GCSE (9-1) Foundation (UK) | A: Graphs | A12: Sketching Graphs of Functions | Graphs of Cubics |

CBSE IX (India) | Algebra | Polynomials | Constant, linear, quadratic and cubic |

CIE IGCSE (9-1) Maths (0626 UK) | 2 Algebra and Graphs | B2.10 Further Graphing | Graphs of Cubics |

Edexcel GCSE (9-1) Foundation (UK) | A: Graphs | A12: Sketching Graphs of Functions | Graphs of Cubics |

GCSE Higher (UK) | Algebra | Graphs | Cubic curves |

OCR GCSE (9-1) Foundation (UK) | 7: Graphs of Equations and Functions | 7.01c: Polynomials and Exponential Functions | Graphs of Cubics |

Universal (all site questions) | G | Graphs | Cubic curves |