A hovercraft takes off from a platform.

Question

Its height (in meters),
\[x\] seconds after takeoff, is modeled by:
\[h(x)=-3(x-3)^2+108\]
What is the height of the hovercraft at the time of takeoff?
meters

Answer 1

To find the height of the hovercraft at the time of takeoff, we need to evaluate the height function \( h(x) \) at \( x = 0 \).

The height function is given by:

\[ h(x) = -3(x-3)^2 + 108 \]

Now, substitute \( x = 0 \):

\[ h(0) = -3(0-3)^2 + 108 \]

Calculate \( (0-3)^2 \):

\[ (0-3)^2 = (-3)^2 = 9 \]

Now substitute this value back into the equation:

\[ h(0) = -3 \cdot 9 + 108 \] \[ h(0) = -27 + 108 \] \[ h(0) = 81 \]

Therefore, the height of the hovercraft at the time of takeoff is \( \boxed{81} \) meters.