document.write( "Question 16327: I was wondering if someone could help me with this one.
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\n" ); document.write( "For fireworks that are launched into the air, the formula
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\n" ); document.write( " h = -16t^2 + 200t + 4
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\n" ); document.write( "models the fireworks' height h, in feet, t seconds after they are launched.
\n" ); document.write( "When should the fireworks explode so that they go off at the greatest height?
\n" ); document.write( "What is that height?
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Algebra.Com's Answer #7960 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
The equation: $\"h+=+-16t%5E2+%2B+200t+%2B+4\"$ describes a parabola. You need to find the location of the vertex of this parabola which will be a maximum since the parabola opens downwards (-16t^2). The horizontal coordinate (t-component) of the vertex is given by: $\"-b%2F2a\"$ . This corresponds to the time, t, at which the firework will reach its maximum height.\r
\n" ); document.write( "\n" ); document.write( "So, the maximum height will occur at: $\"-200%2F2%28-16%29\"$ = $\"25%2F4\"$ secs = 6.25 seconds. This is when the firework should be detonated for it to explode at the greatest height.
\n" ); document.write( "To find this maximum height, substitute t = 6.25 into the original equation and solve for the height, h. It's easier to use the fractional form, 25/4\r
\n" ); document.write( "\n" ); document.write( " $\"h+=+-16%2825%2F4%29%5E2+%2B+200%2825%2F4%29+%2B+4\"$
\n" ); document.write( " $\"h+=+-16%28625%2F16%29+%2B+50%2825%29+%2B+4\"$
\n" ); document.write( " $\"h+=+-625+%2B+1250+%2B+4\"$
\n" ); document.write( " $\"h+=+629\"$ feet. \n" ); document.write( "

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