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C1 Topic 2: Algebra
Completing the square 2 backmore
All these quadratic functions have been expressed in "completed square" form:
x^2 + 4x + 1 = (x+2)^2 - 3
x^2 + 6x + 1 = (x+3)^2 - 8
x^2 - 4x + 3 = (x-2)^2 - 1
x^2 - 8x - 2 = (x-4)^2 - 18
x^2 + 12x + 40 = (x+6)^2 + 4
The display below shows how completing the square is done. You can change the quadratic function and then see the process, step by step.



Summary
Practise completing the square until you become confident in doing it. It is used in mathematics to figure out the maximum and minimum values of a quadratic function. For example, suppose f(x) = x2+6x+1, then because x2+6x+1 = (x+3)2-8 we can state that the minimum value of f(x) is -8, and this occurs when x = -3.
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