document.write( "Question 61942: i really need help with this but no one has responded...is there anyone who can help? PLEASE!\r
\n" ); document.write( "\n" ); document.write( "fireworks are launched into the air. the quadratic function that models the fireworks height, s(x), in feet, x seconds after they are launched is given by the equation s(x)=-16x^2+200x+4. when should the fireworks explode so that they go off at the greatest height? What is that height? \n" ); document.write( "
Algebra.Com's Answer #42658 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
The function that relates the height, h, (in feet) of an object propelled upwards as a function of time, t, (in seconds) is given by:
\n" ); document.write( "\"h%28t%29+=+-16t%5E2+%2B+Vot+%2B+Ho\" where: Vo is the initial upward velocity and Ho is the initial height of the object.\r
\n" ); document.write( "\n" ); document.write( "When graphed, the given quadratic equation will yield a parabola that opens downward. So to answer the question, you will need to find the maximum value of the function s(x).
\n" ); document.write( "The maximum value is at the vertex of the parabola and this is given by \"-b%2F2a\". The a and b come from the general form of the quadratic equation: \"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\".
\n" ); document.write( "In this problem, a = -16 and b= 200, so the x-coordinate of the vertex is:
\n" ); document.write( "\"-200%2F2%28-16%29+=+6.25\" \r
\n" ); document.write( "\n" ); document.write( "The maximum height reached by the firework is attained at time, t = 6.25 seconds and that is when the explosion should occur.
\n" ); document.write( "To find the height at t = 6.25 seconds, substitute t = 6.25 into the quadratic equation and solve for s.
\n" ); document.write( "\"h%286.25%29+=+-16%286.25%29%5E2+%2B+200%286.25%29+%2B+40\"
\n" ); document.write( "\"h%286.25%29+=+-625+%2B+1250+%2B+4\"
\n" ); document.write( "\"h%286.25%29+=+629\"feet.
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