81 meters.
Step-by-step explanation:
The height (in meters), h(x) of a hovercraft x seconds after takeoff, is modeled by:
![h(x)=-3(x-3)^2+108](/tpl/images/0660/1323/8953c.png)
We are to determine its height at the time of takeoff.
Now, at the time of takeoff, x=0.
We substitute x=0 to solve for h.
![h(0)=-3(0-3)^2+108\\=-3(-3)^2+108\\=-3(9)+108\\=-27+108\\=81$ meters](/tpl/images/0660/1323/1422a.png)
The height of the hovercraft at takeoff is 81 meters.