Completing the Square Flashcards

GCSE Mathematics (Edexcel) 1MA1

Completing the square

A method used to rewrite a quadratic expression in the form (x + p)² + q.

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Completing the square

A method used to rewrite a quadratic expression in the form (x + p)² + q.

Standard form of a quadratic expression

ax² + bx + c, where a, b, and c are constants.

Form of a quadratic after completing the square

a(x + p)² + q, where p and q are constants.

Purpose of completing the square

To rewrite a quadratic expression to make it easier to solve or graph.

Step 1 of completing the square

Factorise out the coefficient of x² (if it is not 1) from the x² and x terms.

Step 2 of completing the square

Take half the coefficient of x, square it, and add and subtract this value inside the brackets.

Step 3 of completing the square

Simplify the expression by combining constants outside the brackets.

Vertex form of a quadratic equation

y = a(x + p)² + q, where (-p, q) is the vertex of the parabola.

How to find the turning point using completing the square

The turning point is (-p, q) from the completed square form a(x + p)² + q.

Solving a quadratic by completing the square

Rewrite the quadratic in completed square form, set it equal to 0, and solve for x.

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