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

Set h(x) to 0: To find when the hovercraft lands, set h(x) to 0 and solve for x. 0 = -3(x - 3)^2 + 108Simplify the equation: Divide both sides by -3 to simplify the equation. 0 = (x - 3)^2 - 36Isolate the squared term: Add 36 to both sides to isolate the squared term. (x - 3)^2 = 36Solve for x - 3: Take the square root of both sides to solve for x - 3. x - 3 = ±6Solve for x: Add 3 to both sides to solve for x. x = 3 ± 6Identify solutions: There are two solutions: x = 3 + 6 and x = 3 - 6. x = 9 or x = -3Final determination: Since time cannot be negative, the hovercraft lands after 9 seconds.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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), $x$ seconds after takeoff, is modeled by: $h(x)=-3(x-3)^{2}+108$ $\newline$ How many seconds after takeoff will the hovercraft land on the ground? $\newline$ $\square$ seconds

View step-by-step help

Home

Math Problems

Algebra 2

Solve quadratic equations: word problems

Full solution

Q. A hovercraft takes off from a platform.

\newline

Its height (in meters),

x

seconds after takeoff, is modeled by:

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

\newline

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

\newline

\square

seconds

Set $h(x)$ to $0$ : To find when the hovercraft lands, set $h(x)$ to $0$ and solve for $x$ . $0 = -3(x - 3)^2 + 108$
Simplify the equation: Divide both sides by $-3$ to simplify the equation. $\newline$ $0 = (x - 3)^2 - 36$
Isolate the squared term: Add $36$ to both sides to isolate the squared term. $\newline$ $(x - 3)^2 = 36$
Solve for $x - 3$ : Take the square root of both sides to solve for $x - 3$ . $x - 3 = \pm 6$
Solve for x: Add $3$ to both sides to solve for $x$ . $\newline$ $x = 3 \pm 6$
Identify solutions: There are two solutions: $x = 3 + 6$ and $x = 3 - 6$ . $\newline$ $x = 9$ or $x = -3$
Final determination: Since time cannot be negative, the hovercraft lands after $9$ seconds.