Quadratic relations

Question

The path of a soccer ball can be shown by the equation h=-4t^2+16t where h is in meters and t is in seconds 

find the zeroes of the the quadratic relation 

when does  ball hit the ground 

what is the max height of the ball 

 

Answer 1

h(t) = -4t² + 16t

 

Factor out a -4:

 

     h(t) = -4t(t - 4)

 

The zeros (h(t) = 0) occur when t = 0 and t = 4 sec.  The ball is at ground level when h(t) = 0, which occurs when t = 0 (before you kick the ball) and at t=4 seconds (when it lands after you kick it).

 

The ball reaches its maximum height at the parabola's vertex at time t = -b/2a where a = -4 and b = 16:

 

     t = -16/(2*(-4)) = 2 sec

 

The ball's height at maximum is:

 

     h(t=2) = -4*2² + 16*2 = -16 + 32 = 16 feet