Let h(x)=−x2+4x−1.
(i) Express h(x) in the form −(x−a)2+b.
(ii) Hence write the coordinates of the vertex of the parabola y=h(x).
(iii) Find the equation of the axis of symmetry.
(iv) State the domain of h.
(v) Determine the range of h.
(vi) Sketch a rough graph of y=h(x), showing clearly the vertex, the axis of symmetry and all intercepts with the coordinate axes.