A parabola passes through the points (1,2), (−1,6) and (3,2).
(i) Obtain the quadratic function f(x)=ax2+bx+c that passes through the three given points.
(ii) Using your result from part (i), find the coordinates of the vertex and the equation of the axis of symmetry.
(iii) Comment on the concavity of the parabola and determine the extremum value of f(x) at the vertex.