The vertical displacement (in metres) of a ball thrown upward from ground level is modeled by the polynomial s(t)=−t3+6t2−9t, where t is the time in seconds after the ball is released.
(a) Determine the y-intercept of the graph of s and interpret its physical meaning in this situation.
(b) Factorise s(t) completely over the real numbers.
(c) Calculate all x-intercepts of s and interpret each in the context of the motion of the ball.
(d) Using only the intercepts found in part (iii), state the interval(s) of time during which the ball is above the point of release.