Question 967064: Ricardo throws a stone off a bridge into a river below. The stone's height above the water in meters, y, is dependent on time in seconds after throwing, x, and can be modeled with the function y=−5(x−8)(x+4).
How many seconds after being thrown will the stone hit the water? seconds
What is the maximum height that the stone will reach? meters
How many seconds after being thrown will the stone reach its maximum height? seconds
What is the height of the stone at the time it is thrown? meters
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Ricardo throws a stone off a bridge into a river below. The stone's height above the water in meters, y, is dependent on time in seconds after throwing, x, and can be modeled with the function
y=−5(x−8)(x+4)
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y = -5(x^2 -4x -32) = -5x^2 + 20x + 160
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How many seconds after being thrown will the stone hit the water? seconds
Solve -5(x-8)(x+4) = 0
Ans: x = 8 seconds
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What is the maximum height that the stone will reach? meters
Vertex occurs at x = -b/(2a) = -20/(-10) = 2 seconds
Max height = f(2) = -5(-6)(6) = 180 meters
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How many seconds after being thrown will the stone reach its maximum height? seconds
Ans: 2 seconds (from vertex work above)
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What is the height of the stone at the time it is thrown?
Ans: f(0) = 160 meters
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Cheers,
Stan H.
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