Question

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.

Answer 1

The ball will hit the ground 3seconds later

Explanation:

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.

Answer 2

Answer: t = 3seconds

Explanation:

To find the zero means we will equate the function to zero and then solve, that is

`-16t^(2)`+ 32t + 48 = 0

by factorizing , we have

(t+1)(-16t+48) = 0

Therefore:

t = -1 or t = 3

since time can not be negative , then , t = 3 seconds