document.write( "Question 553801: The equation that describes the path of a rocket after it is shot in the air is $\"h=80t-16t%5E2\"$ , where h is the height, in feet, above the ground after t seconds. After how many seconds will the rocket be at a height of 96 feet? \n" ); document.write( "

Algebra.Com's Answer #361077 by Earlsdon(6294) $\"\"$ $\"About$

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Set h = 96 and solve the quadratic equation for t.
\n" ); document.write( " $\"96+=+80t-16t%5E2\"$ Subtract 96 from both sides and rearrange.
\n" ); document.write( " $\"16t%5E2-80t%2B96+=+0\"$ Factor 16 to ease calculations.
\n" ); document.write( " $\"16%28t%5E2-5t%2B6%29+=+0\"$ Factor the trinomial.
\n" ); document.write( " $\"t%5E2-5t%2B6+=+%28t-2%29%28t-3%29\"$
\n" ); document.write( " $\"%28t-2%29%28t-3%29+=+0\"$ Apply the zero product rule:
\n" ); document.write( " $\"t-2+=+0\"$ or $\"t-3+=+0\"$ so:
\n" ); document.write( " $\"t+=+2\"$ or $\"t+=+3\"$
\n" ); document.write( "You have two solutions for this problem which was to be expected because quadratics have two solutions.
\n" ); document.write( "At t = 2 seconds, the rocket reaches a height of 96 feet on the way up.
\n" ); document.write( "At t = 3 seconds, it will pass the 96-foot level on the way down. \n" ); document.write( "

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