Answer:
3 seconds
Step-by-step explanation:
Since h(t) represents the height and t represents the time, we can set the equation equal to 150 to find t.
-16t^2+96t+6=150
Subtract 150 from both sides to set the equation equal to 0, to find the solutions.
-16t^2+96t-144=0
Factor out -16, because all of the terms are divisible by it.
-16(t^2+6t+9)=0
Now we can focus on the terms inside the parenthesis and factor it again.
t^2-6t+9=0
We need to find two value that can be multiplied to get 9 and added to get -6.
-3 and -3 works.
Thus, we get (x-3)(x-3).
Now solve for 0.
x-3=0
x=3
The object reaches its maximum height after 3 seconds.