You might need: Calculator A hovercraft takes off from a platform. Its height (in meters), \( x \) seconds after takeoff, is modeled by: \( h(x)=-3(x-3)^{2}+108 \) How many seconds after takeoff will the hovercraft land on the ground? seconds

To find out when the hovercraft lands on the ground, we set the height function \( h(x) \) equal to 0: \[ 0 = -3(x-3)^{2} + 108 \] Solving for \( x \): 1. Rearranging gives us \( 3(x-3)^{2} = 108 \). 2. Dividing by 3: \( (x-3)^{2} = 36 \). 3. Taking the square root: \( x-3 = 6 \) or \( x-3 = -6 \). 4. So, \( x = 9 \) or \( x = -3 \). Since time cannot be negative, the hovercraft will land on the ground \( 9 \) seconds after takeoff. 9 seconds.