Question 322777: The path of a toy rocket is defined by the relation y=-3x^2+11x+4, where x is the horizontal distance, in meters, traveled and y is the height, in metres, above the ground.
Determine the zeros of the relation.
How far has the rocket traveled horizontally when it lands on the ground?
What is the maximum height of the rocket above the ground, to the nearest hundredth of a meter?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The path of a toy rocket is defined by the relation y=-3x^2+11x+4, where x is the horizontal distance, in meters, traveled and y is the height, in metres, above the ground.
Determine the zeros of the relation.
-3x^2 + 11x + 4 = 0
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3x^2 - 11x -4 = 0
Factor:
3x^2 - 12x + x - 4 = 0
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3x(x-4) + x-4 = 0
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(x-4)(3x+1) = 0
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x = 4 or x = -1/3
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f(x) = -3x^2+11x+4
How far has the rocket traveled horizontally when it lands on the ground?
4 ft.
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What is the maximum height of the rocket above the ground, to the nearest hundredth of a meter?
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max occurs when x = -b/2a = -11/(2*-3) = 11/6
height = f(11/6) = 14.083 ft
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Cheers,
Stan H.
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