Quadratic Functions

Quadratic functions are polynomials of degree 2 with the general form f(x) = ax² + bx + c, where a ≠ 0. This lesson covers solving quadratics, completing the square, the discriminant, and sketching parabolas — all essential for the Edexcel 9MA0 specification.

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Forms of a Quadratic

Form	Expression	Key Information
General form	ax² + bx + c	Coefficients visible; y-intercept is c
Factorised form	a(x − p)(x − q)	Roots are x = p and x = q
Completed square	a(x − h)² + k	Vertex at (h, k); line of symmetry x = h

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Solving Quadratic Equations

Method 1: Factorisation

If ax² + bx + c can be written as a product of two linear factors, set each factor to zero.

Example: Solve x² − 5x + 6 = 0.

• (x − 2)(x − 3) = 0
• x = 2 or x = 3

Example: Solve 6x² + x − 2 = 0.

• (2x − 1)(3x + 2) = 0
• x = 1/2 or x = −2/3