(a) Divide \(\frac{x^{2} - 4}{x^{2} + x}\) by \(\frac{x^{2} - 4x + 4}{x + 1}\). (b) The diagram below shows the graphs of \(y = ax^{2} + bx + c\) and \(y = ...

(a) Divide \(\frac{x^{2} - 4}{x^{2} + x}\) by \(\frac{x^{2} - 4x + 4}{x + 1}\).

(b) The diagram below shows the graphs of \(y = ax^{2} + bx + c\) and \(y = mx + k\) where a, b, c and m are constants. Use the graph(s) to :

(i) find the roots of the equation \(ax^{2} + bx + c = mx + k\); 

(ii) determine the values of a, b and c using the coordinates of points L, M and N and hence write down the equation of the curve;

(iii) determine the line of symmetry of the curve \(y = ax^{2} + bx + c\).