f(x) = a(x + b)2 + c 1 4 5 2 -2 -4 2 1 e.g. use coefficients to 1 4 5 2 -2 -4 2 1 e.g. use coefficients to factorise further if possible !! Factor Theorem 2x2 - 8x + 9 (x+2) is a factor since no remainder Remember to answer question f(x) = ( ) ( ) ( ) 2x2 - 8x + 9 Completing the square 2(x2 - 4x) + 9 Factorising cubic's polynomials 2(x - 2)2 + 9 - 8 Quadratic Theory questions (Circle, Function Graphs) f(x) = 2(x - 2)2 + 1 simultaneous equations Sketch See Function & Graphs Harder Finding coefficients Discriminant b2 – 4ac 3 scenarios Steps Identify a , b and c. Discriminant .... = 0 and factorise. Sketch and identify solution based on question asked. Harder discriminant > 0 = 0 tangent !!! < 0 (1 - 2k)x2 - 5kx - 2k > 0