document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #31925 by Earlsdon(6294) $\"\"$ $\"About$

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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.
\n" ); document.write( "So if you can find the value of h at the vertex, you will have found the maximum height attained by the object, right?
\n" ); document.write( "Let's rewrite the equation in function form as:
\n" ); document.write( " $\"h%28t%29+=+-16t%5E2%2B32t\"$ Compare this with the standard form for a quadratic equation:
\n" ); document.write( " $\"y+=+ax%5E2%2Bbx%2Bc\"$ so in your equation, a = -16, b = 32, and c = 0\r
\n" ); document.write( "\n" ); document.write( "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:
\n" ); document.write( " $\"t+=+%28-32%29%2F%282%28-16%29%29\"$
\n" ); document.write( " $\"t+=+1\"$ second. \n" ); document.write( "

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