detailed solution

ITEM 4: [Maximum mark: 15] Let f(x) = 2x2 + 4r + p, for r E R, where pe Z. (a) The equation f(z) = 0 has two equal roots. (i) Write down the value of the discriminant of f. (ii) Show that p = 2. 13 (b) For the graph of f, find: (i) the equation of the axis of symmetry. (ii) the coordinates of the vertex; [4] (c) -Write down the solution to the equation f(z) = 0. [1] (d) The function f can be written in the form /(x) = a(2 -h) + k. Find the values of a, and k. [5] (e) The graph of a function g is obtained from the graph of f by a reflection in the z-axis. Find the coordinates of the vertex of the graph of g