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

Understand the Problem: Understand the problem. We need to find the time when the hovercraft's height is 0, which means it has landed on the ground. The height is given by the function h(x) = -3(x - 3)² + 108.Set Height Function: Set the height function equal to 0 to find when the hovercraft lands. 0 = -3(x - 3)² + 108Solve for x: Solve for x. First, move the constant term to the other side of the equation: -3(x - 3)² = -108Isolate Squared Term: Divide both sides by -3 to isolate the squared term. (x - 3)² = 36Solve for x: Take the square root of both sides to solve for x - 3. x - 3 = ±6Discard Negative Value: Solve for x by adding 3 to both possible values of x - 3. x = 3 + 6 or x = 3 - 6 x = 9 or x = -3Since time cannot be negative, we discard the negative value. The hovercraft will land on the ground after 9 seconds.

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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

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

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Q. A hovercraft takes off from a platform.

\newline

Its height (in meters),

\newline

x

seconds after takeoff, is modeled by:

\newline

h(x)=-3(x-3)^{2}+108

\newline

How many seconds after takeoff will the hovercraft land on the ground?

\newline

\text{seconds}

Understand the Problem: Understand the problem. $\newline$ We need to find the time when the hovercraft's height is $0$ , which means it has landed on the ground. The height is given by the function $h(x) = -3(x - 3)^2 + 108$ .
Set Height Function: Set the height function equal to $0$ to find when the hovercraft lands. $\newline$ $0 = -3(x - 3)^2 + 108$
Solve for x: Solve for x. $\newline$ First, move the constant term to the other side of the equation: $\newline$ $-3(x - 3)^2 = -108$
Isolate Squared Term: Divide both sides by $-3$ to isolate the squared term. $\newline$ $(x - 3)^2 = 36$
Solve for x: Take the square root of both sides to solve for $x - 3$ . $x - 3 = \pm 6$
Discard Negative Value: Solve for $x$ by adding $3$ to both possible values of $x - 3$ .
$x = 3 + 6$ or $x = 3 - 6$
$x = 9$ or $x = -3$
Discard Negative Value: Solve for $x$ by adding $3$ to both possible values of $x - 3$ .
$x = 3 + 6$ or $x = 3 - 6$
$x = 9$ or $x = -3$ Since time cannot be negative, we discard the negative value.
The hovercraft will land on the ground after $9$ seconds.