Question 964462: A hovercraft takes off from a platform. Its height in meters, y, is dependent on the number of seconds after takeoff, x, and can be modeled with the function y=−3(x−3)^2+108
How many seconds after takeoff will the hovercraft reach its maximum height?
....... seconds
What is the maximum height that the hovercraft will reach?
......... meters
How many seconds after takeoff will the hovercraft land on the ground?
.......... seconds
What is the height of the hovercraft at the time of takeoff?
.......... meters
Found 2 solutions by lwsshak3, rothauserc:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A hovercraft takes off from a platform. Its height in meters, y, is dependent on the number of seconds after takeoff, x, and can be modeled with the function
y=−3(x−3)^2+108
This is an equation of a parabola that opens downward with vertex at (3,108)
..
How many seconds after takeoff will the hovercraft reach its maximum height?
..3... seconds
What is the maximum height that the hovercraft will reach?
..108.... meters
..
How many seconds after takeoff will the hovercraft land on the ground?
...9.... seconds
set y=0
−3(x−3)^2+108=0
−3(x−3)^2=-108
divide both sides by -3
(x−3)^2=36
take sqrt of both sides
x-3=±√36=±6
x=3±6
x=9
..
What is the height of the hovercraft at the time of takeoff?
...81.... meters
set x=0
−3(x−3)^2+108=-27+108=81
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! y = −3(x−3)^2 +108
y = -3(x^2 -6x +9) +108
y = -3x^2 +18x -27 +108
y = -3x^2 +18x +81
Note This is a parabola that opens downward, therefore we want the coordinates of the vertex,
x = -b/2a = -18 / 2(-3) = 3
now substitute x = 3 in the equation above
y = -3(3^2) +18(3) +81
y = -27 +54 +81
y = 108
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1) hovercraft reaches maximum height in 3 seconds
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2) maximum height is 108 meters
*******************************
3) -3x^2 +18x +81 = 0
(-3x-9)(x-9) = 0
-3x = 9
x = -3 and x = 9
we want the positive value for x
The hovercraft will land on the ground in 9 seconds
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4) y = -3x^2 +18x +81
substitute x = 0
y = 81
The hovercraft is at a height of 81 meters at time 0 seconds
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