Consider the quadratic function f(x)=3x2−7x+4.
a. (i) Rewrite f(x) in the form a(x−h)2+k.
b. (ii) Hence determine the coordinates of the vertex and the equation of the axis of symmetry of the parabola y=f(x).
c. (iii) State the minimum value of f(x) and the value of x at which this minimum occurs.