SOLUTION: If an object on Earth is propelled upward with an initial velocity of 32 ft. per second, then its height is given by h=32t-16t^2. After how many seconds does it reach its mamimum h

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Question 48257: If an object on Earth is propelled upward with an initial velocity of 32 ft. per second, then its height is given by h=32t-16t^2. After how many seconds does it reach its mamimum height?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
One approach to the solution to this problem is to recognise that that path described by the object is that of a parabbola which opens downward. The maximum height reached by the object will be at the vertex of the parabola.
So if you can find the value of h at the vertex, you will have found the maximum height attained by the object, right?
Let's rewrite the equation in function form as:
h%28t%29+=+-16t%5E2%2B32t Compare this with the standard form for a quadratic equation:
y+=+ax%5E2%2Bbx%2Bcso in your equation, a = -16, b = 32, and c = 0
The x-coordinate (or t-coordinate in your problem) of the vertex is given by: x+=+%28-b%29%2F2a, in your problem, this would be:
t+=+%28-32%29%2F%282%28-16%29%29
t+=+1second.