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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

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 $Y1 = AX$x2$+BX+C$
  • Then select the GRAPH screen.
  • You can then choose different values for the constants.
  • For example, to make $A$ = $1$ press $1$ STO➧ ALPHA $A$.

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


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.

This page also uses the MathJax system for displaying maths symbols.


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.

quadratic

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

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AP Calculus AB (USA)2Algebra and FunctionsQuadratic curves-
AP Calculus BC (USA)2Algebra and FunctionsQuadratic curves-
AQA A-Level (UK - Pre-2017)C1Algebra and FunctionsQuadratic curves-
AQA AS Maths 2017Pure MathsAlgebraQuadratic Curves-
AQA AS/A2 Maths 2017Pure MathsAlgebraQuadratic Curves-
CBSE IX (India)AlgebraPolynomialsConstant, linear, quadratic and cubic-
CCEA A-Level (NI)C1Algebra and FunctionsQuadratic curves-
CIE A-Level (UK)P1Algebra and FunctionsQuadratic curves-
Edexcel A-Level (UK - Pre-2017)C1Algebra and FunctionsQuadratic curves-
Edexcel AS Maths 2017Pure MathsQuadraticsQuadratic Curves-
Edexcel AS/A2 Maths 2017Pure MathsQuadraticsQuadratic Curves-
I.B. Higher Level2Algebra and FunctionsQuadratic curves-
I.B. Standard Level2Algebra and FunctionsQuadratic curves-
Methods (UK)M1Algebra and FunctionsQuadratic curves-
I.B. (MSSL)4Algebra and FunctionsQuadratic curves-
OCR A-Level (UK - Pre-2017)C1Algebra and FunctionsQuadratic curves-
OCR AS Maths 2017Pure MathsEquations and QuadraticsQuadratic Curves-
OCR MEI AS Maths 2017Pure MathsQuadraticsQuadratic Curves-
OCR-MEI A-Level (UK - Pre-2017)C1Algebra and FunctionsQuadratic curves-
Pre-U A-Level (UK)1Algebra and FunctionsQuadratic curves-
Scottish (Highers + Advanced)HM1Algebra and FunctionsQuadratic curves-
Scottish HighersM1Algebra and FunctionsQuadratic curves-
Universal (all site questions)AAlgebra and FunctionsQuadratic curves-
WJEC A-Level (Wales)C1Algebra and FunctionsQuadratic curves-