AS-level Edexcel Pure Maths - Module 2: Quadratics|2023 LATEST UPDATE|GUARANTEED SUCCESS

Quadratic equation Written as ax²+bx+c=0 where a, b, c and constants. Has 0-2 solutions Roots - The solutions to an equation - The values of x for which f(x)=0 - Find by factorising x Completing the square x²+bx = (x+b÷2)²-(b÷2)² Completing the square when a≠1 - Factorise as much as possible - Otherwise keep a outside the brackets Completing the square when a≠1 - method 2x²-12x = 2(x²-6x) = 2((x-3)²-3²) Complete the square = 2((x-3)²-9) Simplify = 2(x-3)²-18 Multiply outside bracket by a Domain The set of possible inputs of a function Find through substitution Range The set of possible outputs of a function Find through completing the square ∈ Symbol meaning 'a member of' b²-4ac Discriminant Parabola The shape of a quadratic graph Y-intercept, roots, turning point Values for drawing quadratics f(x) has 2 roots b²-4ac > 0 f(x) has 1 root b²-4ac = 0 f(x) has no roots b²-4ac < 0 Mathematical model A mathematical description of a real life situation Quadratic formula ax²+bx+c a(x+b÷2a)²+(c-b²÷4a)