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 $\boxed{{\displaystyle 81}}$ meters.