Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 48feet above the ground,
the function h(t)=−16t2+32t+48 models the height, h, of the ball above the ground as a function of time, t. Find the zero of this function that tells us when the ball will hit the ground.
Given the function that model the height to be h(t)=−16t2+32t+48, the zero of this function can be evaluated equating the function to zero i.e h(t) = 0
0 =−16t2+32t+48
-t²+2t+3 = 0
Multiplying through by minus
t²-2t-3 = 0
Factorising the function to get t;
t²-3t+t-3 = 0
(t²-3t)+1(t-3) = 0
t(t-3)+1(t-3) = 0
(t-3)(t+1) = 0
t-3 = 0 and t+1 = 0
t = 3secs and -1sec
Since the time cannot be negative, the zero of the function is 3seconds which is the time taken by the ball to hit the ground.
