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