SOLUTION: An object is throwen 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 x

Question 10673: An object is throwen 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 x squared. Find the objects maximum height.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!

This is the equation of the height of an object propelled upward at an intial velocity of 400 ft/sec at an initial height of zero ft. It is usually written as:
Where: h = height and t = time.
The maximum height occurs at the vertex of the parabola whose x-coordinate (or t-value) is given by: . This value of t will be the time at which the object reaches its maximum height. The equation must be in the standard form of:
or, in this case: But here, a = -16, b = 400, and c = 0.
So, = 12.5 secs. The time at maximum height.
Now, we substitute this value of t into the original eqation and solve for h to get the maximum height.
= 2500 feet. This is the maximum height attained by the object.

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