During a community fair, an entrance arch was constructed. the shape of the arch can be represented by the polynomial \(p(x) = -x^2 + 2x + 8\), where \(x\) is the length(in feet) on stage level.
Based on the figure given above, answer the following questions:
(i) Find the height of the arch.
(ii) Determine zeroes of the polynomial \(p(x)\).
(iii) Find 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.