A quadratic polynomial g(x) has its axis of symmetry at x=2 and opens downwards. The curve passes through the points (0,−3) and (4,−3), and it meets the x–axis at exactly one point.
(i) Draw a rough sketch of the graph of y=g(x), clearly showing the vertex, the axis of symmetry and the given points.
(ii) From your sketch, decide how many real zeros g(x) possesses and indicate the approximate value of the zero on the x–axis.
(iii) Determine the exact zero of g(x) algebraically and compare it with the value obtained in part (ii).