Question
A hovercraft takes off from a platform.
Its height (in meters),
\[x\] seconds after takeoff, is modeled by:
\[h(x)=-3(x-3)^2+108\]
What is the height of the hovercraft at the time of takeoff?
meters
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
Answers
Answered by
GPT-4o mini
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.
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.