ASMaths: PureAQARevision Notes2. Algebra & Functions2.2 Quadratics2.2.1 Quadratic Graphs

Quadratic Graphs (AQA AS Maths: Pure)

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Quadratic Graphs

What are quadratic graphs?

  • The general equation of a quadratic graph is y space equals space a x squared plus b x plus c 
  • Their shape is called a parabola ("U" shape)
  • Positive quadratics have a value of  a space greater than 0 so the parabola is uprightunion
  • Negative quadratics have a value of a less than 0 so the parabola is upside down intersection

Quadratic Graphs Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

Using quadratic graphs

You need to be able to:

  • sketch a quadratic graph given an equation or information about the graph
  • determine, from the equation, the axes intercepts
  • factorise, if possible, to find the roots of the quadratic function 
  • find the coordinates of the turning point (maximum or minimum)
You may have to rearrange the equation before you can find some of these things
Quadratic Graphs Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

Examiner Tip

  • Your calculator may tell you the roots of a quadratic function and the coordinates of the turning point
  • But don't rely on it – think about how many marks the question is worth and how much method/working you should show
  • Remember sometimes you'll need to rearrange an equation into the form y space equals space a x squared plus b x plus c

Worked example

2-2-1-quadratic-graphs-example-diagram2-2-1-quadratic-graphs-example-diagram-1

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    Paul

    Author: Paul

    Expertise: Maths

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.