During a school festival, a decortive arch was installed at the entrance. The shape of the arch can be represented by the polynomial \(p(x) = -x^2 + 2x + 8\), where \(x\) is the horizontal distance (in feet) from one end of the arch.
Based on the figure given above, answer the following questions:
(i) Find the height of the arch.
(ii) Find zeroes of the polynomial \(p(x)\).
(iii) Calculate the span of the arch on the stage floor.
(iv) Write the coordinates of the point of intersection of the above curve with the \(y-\)axis.