completing the square
What completing the square means in Mathematics GCSE, as defined for AQA, Pearson Edexcel.
Definitions of completing the square
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Reference: AQA
Rewriting a quadratic from expanded form into vertex form, halving the coefficient of x inside the bracket and subtracting the square of that half from the constant.
Writing a quadratic as y = (x + p)² + q, halving the coefficient of x and adjusting the constant outside the bracket by the square that was added.
Writes x² + bx + c as (x + b/2)² - (b/2)² + c, including when the coefficient of x² is not 1, by factoring out that coefficient first.
Rewriting a quadratic such as x² + 6x + 2 = 0 as (x + 3)² − 7 = 0, so that (x + 3)² = 7 and x = −3 ± √7.
Topics that use completing the square
- Graphs (AQA GCSE)
- Solving equations and inequalities (AQA GCSE)
- Algebra - Graphs (Pearson Edexcel GCSE)
- Algebra - Solving equations and inequalities (Pearson Edexcel GCSE)
Related terms
Using completing the square in the exam
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