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Question 348281: The equation y = 0.5x - .01x^2 represents the parabolic flight of a certain cannonball shot at an angle of 26 degrees with the horizon and an initial velocity of 25 meters per second. In this equation, y is the height of the cannonball, in meters, and the x is the vertical distance traveled, in meters. Given the coordinates of (10,4) and (40,4) lie on the parabola, at what x-coordinate must the vertex lie?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The equation y = 0.5x - .01x^2 represents the parabolic flight of a certain cannonball shot at an angle of 26 degrees with the horizon and an initial velocity of 25 meters per second. In this equation, y is the height of the cannonball, in meters, and the x is the vertical distance traveled, in meters. Given the coordinates of (10,4) and (40,4) lie on the parabola,
at what x-coordinate must the vertex lie?
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What the question wants you to notice is the symmetry of the two
given points. They are both at y = 4 and separated by (40-10) = 30
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The symmetry line is half between 40 and 10; that is 25.
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So the x-coordinate of the vertex is x = 25.
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Check it out:
y = -0.01x^2 + 0.5x
a = -0.01 ; b = 0.5
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-b/2a = -0.5/(2*-0.01) = 0.5/0.02 = 25
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Cheers,
Stan H.
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