SOLUTION: An object is thrown from the origin of a coordinate system with the x-axis along the ground and the y-axis vertical. Its path, or trajectory, is given by the equation y = 400x – 16

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Question 669843: An object is thrown from the origin of a coordinate system with the x-axis along the ground and the y-axis vertical. Its path, or trajectory, is given by the equation y = 400x – 16x2.
a. For what value of x does the object reach maximum height?


b. Find the objects maximum height.


Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
y=400x-16x^2
Where: y = height and x = time.
The maximum height occurs at the vertex of the parabola whose x-coordinate is -b%2F2a in the quadratic equation ax^2+bx+c.
a = -16, b = 400, and c = 0.
-b%2F2a%29=+-400%2F-32
=12.6 seconds The time at maximum height.
Substitute this value of x into the original equation and solve for y to get the maximum height.
y=400x-16x%5E2
y=400%2A12.5-16%2812.5%29%5E2
=2500 feet maximum height reached by the object.