document.write( "Question 1158571: A roofer thows a group of shingles into the trash bin on the ground below. The height of the shingles can be modeled by the function h(t)= -5t^2+11t+12 where h(t) is the height in meters and t is the time in seconds\r
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\n" ); document.write( "\n" ); document.write( "b) Determine the maximum height of the shingles?\r
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Algebra.Com's Answer #781511 by Shin123(626) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: Completing the Square for Quadratics

To complete the square for the quadratic $\"-5%2Ax%5E2%2B11%2Ax%2B12=0\"$ , we must first find a square which when expanded, has -5x² and 11x in it.
\n" ); document.write( "Factoring -5 from the left side gives $\"-5%28x%5E2-2.2%2Ax-2.4%29=0\"$ . $\"%28x-1.1%29%5E2\"$ is the square we are looking for. So we get $\"-5%28%28x-1.1%29%5E2-3.61%29=0\"$ .\n" ); document.write( "Taking the -3.61 out of the -5, we get $\"highlight%28-5%28x-1.1%29%5E2%2B18.05%29\"$ . Subtracting 18.05 from both sides, we get $\"-5%28%28x-1.1%29%5E2%29=-18.05\"$ . Since the right side is negative, there are no real solutions.

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Since time can't be negative, it takes 3 seconds for the shingles to hit the trash. The maximum value occurs when $\"-5%28x-1.1%29%5E2\"$ is 0. This happens when x=1.1. The maximum height is 18.05 meters and it occurs after 1.1 seconds has passed. \n" ); document.write( "

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