The function is [tex]h(t) = -16t^2 + 80t + 224[/tex], and according to the description of the function in the problem statement, we have the following:
at t=0 after being thrown (that is, at initial time), the height of the ball is calculated by h(0) as follows:
[tex]h(0) = -16(0)^2 + 80(0) + 224=0+0+224=224[/tex] (ft), which is the initial height, as expected.
At t=1 (sec), the height would be [tex]h(1) = -16(1)^2 + 80(1) + 224=-16+80+224=288[/tex].
etc.
The path is parabolic, as we know by seeing that the function is a quadratic polynomial function. This function has been given in factored form as well. From that we can see that the zeros of the function are t=7 and t=-2.
This means that at t=7 sec, the height h is 0, which means that the ball has hit the ground. t=-2 has no significance in the context of our problem so we just neglect it.
Answer: B) 7 sec
