Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

The Quadratic Function

13 min read

Completing the square, the discriminant, quadratic inequalities, and roots of equations.

The quadratic $ax^2 + bx + c$ underpins much of further maths.

Completing the square

$x^2 + bx + c = \left(x + \tfrac{b}{2}\right)^2 - \left(\tfrac{b}{2}\right)^2 + c$ , giving the vertex.

Worked example. $x^2 - 6x + 11 = (x-3)^2 + 2$ — minimum at $(3, 2)$ .

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Edexcel IGCSE·Further Pure Mathematics·IGCSE Further Pure Mathematics

13 min read

Completing the square, the discriminant, quadratic inequalities, and roots of equations.

The quadratic $ax^2 + bx + c$ underpins much of further maths.

$x^2 + bx + c = \left(x + \tfrac{b}{2}\right)^2 - \left(\tfrac{b}{2}\right)^2 + c$ , giving the vertex.

Worked example. $x^2 - 6x + 11 = (x-3)^2 + 2$ — minimum at $(3, 2)$ .

Create a free account to read this note in full. Every free account gets 2 complete revision notes — no card needed.