Let f(x)=kx2+(k−4)x+1, where k=0. The vertex of the parabola represented by y=f(x) lies on the y-axis.
(i) Determine the value(s) of k that satisfy the given condition.
(ii) For the admissible value of k, find the coordinates of the vertex and the equation of the axis of symmetry.
(iii) State whether the vertex corresponds to a maximum or a minimum value of f(x) and find that value.