Sketching Polynomials (CIE A Level Maths: Pure 1)

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Sketching Polynomials

Sketching the graph of a polynomial

  • Remember a polynomial is any finite function with non-negative indices, that could mean a quadratic, cubic, quartic or higher power

Sketching Polynomials Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

  • When asked to sketch a polynomial you'll need to think about the following
    • y-axis intercept
    • x-axis intercepts (roots)
    • turning points (maximum and/or minimum)
    • a smooth curve (this takes practice!)

How do I sketch a graph of a polynomial?

STEP 1        Find the y-axis intercept by setting x = 0

STEP 2        Find the x-axis intercepts (roots) by setting y = 0

STEP 3        Consider the shape and “start”/”end” of the graph

eg. a positive cubic graph starts in third quadrant (“bottom left”) and “ends” in first quadrant (“top right”)

STEP 4        Consider where any turning points should go

STEP 5        Draw with a smooth curve

 Sketching Polynomials Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes  

Sketching Polynomials Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes 

  • Coordinates of turning points can be found using differentiation
  • Except with a point of inflection, repeated roots indicate the graph touches the x-axis

Worked example

Sketching Polynomials Example Diagram, A Level & AS Level Pure Maths Revision Notes

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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.