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Investigate the effect of changing a and b.
Make sure that you are clear about these aspects of a quadratic graph:
  • its basic shape
  • its symmetry
  • the number of places where the curve crosses the x-axis
  • how the values of a and b affect the shape and position of the curve

Summary/Background

graphic calculator A note about graphic calculators
A graphic calculator is not allowed in your exam. However you can use one for revision. The TI-83, or similar model, can display cubic graphs for you.
Select the Y= screen:
Enter Y1 = (X-A)(X-B)
Then select the GRAPH screen. You can then choose different values for the constants A and B. For example, to make A = 1, press 1 store ALPHA A.
quadratic sketch

Downloadable Files

If your computer is set up with either Omnigraph or Autograph then you can download these files to investigate quadratic curves further.
Autograph - quad02Autograph - quad02
Investigate quadratic curves further using Autograph.
Omnigraph - quad02Omnigraph - quad02
Investigate quadratic curves further using Omnigraph.

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, and uses SVG and VML. JSXGraph is easy to embed and has a small footprint: less than 100 KByte if embedded in a web page. No plug-ins are required! Special care has been taken to optimize the performance.

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.

quadratic

A mathematical expression of the 2nd degree; having a x² term but no higher one.