MathsNet: G - Graphs - Investigate 3

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Page ID: 13671

G | Graphs | Cubic curves | «Investigate 3»

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

JSXGraph

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.

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.

plot

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

Full Glossary List

This question appears in the following syllabi:

Syllabus	Module	Section	Topic	Exam Year
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	-