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 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 $Y1 = AX$x
^{2}$+BX+C$ - 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.

## 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

### function

### graph

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

### quadratic

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AP Calculus AB (USA) | 2 | Algebra and Functions | Quadratic curves | - |

AP Calculus BC (USA) | 2 | Algebra and Functions | Quadratic curves | - |

AQA A-Level (UK - Pre-2017) | C1 | Algebra and Functions | Quadratic curves | - |

CCEA A-Level (NI) | C1 | Algebra and Functions | Quadratic curves | - |

CIE A-Level (UK) | P1 | Algebra and Functions | Quadratic curves | - |

Edexcel A-Level (UK - Pre-2017) | C1 | Algebra and Functions | Quadratic curves | - |

I.B. Higher Level | 2 | Algebra and Functions | Quadratic curves | - |

I.B. (MSSL) | 4 | Algebra and Functions | Quadratic curves | - |

I.B. Standard Level | 2 | Algebra and Functions | Quadratic curves | - |

Methods (UK) | M1 | Algebra and Functions | Quadratic curves | - |

OCR A-Level (UK - Pre-2017) | C1 | Algebra and Functions | Quadratic curves | - |

OCR-MEI A-Level (UK - Pre-2017) | C1 | Algebra and Functions | Quadratic curves | - |

Pre-U A-Level (UK) | 1 | Algebra and Functions | Quadratic curves | - |

Scottish Highers | M1 | Algebra and Functions | Quadratic curves | - |

Scottish (Highers + Advanced) | HM1 | Algebra and Functions | Quadratic curves | - |

WJEC A-Level (Wales) | C1 | Algebra and Functions | Quadratic curves | - |

Universal (all site questions) | A | Algebra and Functions | Quadratic curves | - |

Universal (all site questions) | A | Algebra and Functions | Quadratic curves | - |

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

Edexcel AS/A2 Maths 2017 | Pure Maths | Quadratics | Quadratic Curves | - |

Edexcel AS Maths 2017 | Pure Maths | Quadratics | Quadratic Curves | - |

AQA AS Maths 2017 | Pure Maths | Algebra | Quadratic Curves | - |

OCR AS Maths 2017 | Pure Maths | Equations and Quadratics | Quadratic Curves | - |

OCR MEI AS Maths 2017 | Pure Maths | Quadratics | Quadratic Curves | - |

AQA AS/A2 Maths 2017 | Pure Maths | Algebra | Quadratic Curves | - |