We have been given that a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second then its height H after T seconds is given by the equation [tex]h(t)=-16t^2+128t[/tex] (if air resistance is neglected).
We are asked to find the time when the object will reach its maximum height.
We can see our given equation is a downward opening parabola, so its maximum point will be vertex of parabola.
We know that x coordinate of vertex is [tex]\frac{-b}{2a}[/tex].
We can see from our given equation that [tex]b=128[/tex] and [tex]a=-16[/tex].
[tex]\frac{-b}{2a}=\frac{-128}{2(-16)}=\frac{-128}{-32}=4[/tex]
Therefore, the object will reach its maximum height after 4 seconds and option D is the correct choice.
