Revision Notes

What is completing the square?

Completing the square” is something that can be done to a quadratic expression (to make it easier to work with or more useful in some way)

It involves writing the quadratic expression  x2 + px +q in the form (x + a)2 + b

Why use completing the square?
  • The question might ask you to…
  • You can use it to find the turning point or vertex of a quadratic curve (Parabola) – the turning point is at (−a, b)
  • It’s a way of solving a quadratic equation
How to complete the square?

There are a number of slightly different ways of approaching this.

One simple process is:

  1. HALVE the coefficient of x to find a:  a = ½p
  2. SUBTRACT the square of a from q to find b:  b = q – a2
  3. WRITE DOWN the answer using your values for a and b:  (x + a)2 + b

Special case: If there’s a number in front of x2, m, say, ie. m≠1

  • Divide by m
  • Do steps 1, 2 and 3 above
  • Multiply by m

Example

GCSE Maths revision notes

Question

Edexcel GCSE Maths Notes

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