document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964462>Question 964462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hovercraft takes off from a platform. Its height in meters, y, is dependent on the number of seconds after takeoff, x, and can be modeled with the function y=&#8722;3(x&#8722;3)^2+108<BR>\n" );
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document.write( "How many seconds after takeoff will the hovercraft reach its maximum height? <BR>\n" );
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document.write( "What is the maximum height that the hovercraft will reach?\r<BR>\n" );
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document.write( "......... meters\r<BR>\n" );
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document.write( "How many seconds after takeoff will the hovercraft land on the ground? \r<BR>\n" );
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document.write( ".......... seconds\r<BR>\n" );
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document.write( "What is the height of the hovercraft at the time of takeoff? <BR>\n" );
document.write( ".......... meters\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589353 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589353\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = &#8722;3(x&#8722;3)^2 +108<BR>\n" );
document.write( "y = -3(x^2 -6x +9) +108<BR>\n" );
document.write( "y = -3x^2 +18x -27 +108<BR>\n" );
document.write( "y = -3x^2 +18x +81<BR>\n" );
document.write( "Note This is a parabola that opens downward, therefore we want the coordinates of the vertex,<BR>\n" );
document.write( "x = -b/2a = -18 / 2(-3) = 3<BR>\n" );
document.write( "now substitute x = 3 in the equation above<BR>\n" );
document.write( "y = -3(3^2) +18(3) +81<BR>\n" );
document.write( "y = -27 +54 +81<BR>\n" );
document.write( "y = 108<BR>\n" );
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document.write( "1) hovercraft reaches maximum height in 3 seconds<BR>\n" );
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document.write( "2) maximum height is 108 meters<BR>\n" );
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document.write( "3) -3x^2 +18x +81 = 0<BR>\n" );
document.write( "(-3x-9)(x-9) = 0<BR>\n" );
document.write( "-3x = 9<BR>\n" );
document.write( "x = -3 and x = 9<BR>\n" );
document.write( "we want the positive value for x<BR>\n" );
document.write( "The hovercraft will land on the ground in 9 seconds<BR>\n" );
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document.write( "4) y = -3x^2 +18x +81<BR>\n" );
document.write( "substitute x = 0<BR>\n" );
document.write( "y = 81<BR>\n" );
document.write( "The hovercraft is at a height of 81 meters at time 0 seconds<BR>\n" );
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