document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112413>Question 112413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The word problem I am having troubles with is as follows.....<BR>\n" );
document.write( "    The height (h) (in feet) of a rocket at time (t) seconds after liftoffi sgiven by h=-16t^2+800t.<BR>\n" );
document.write( "(a). how long dos it take the rocket to reach 3200 feet?<BR>\n" );
document.write( "(b). What is the masimum height of the rocket. \r<BR>\n" );
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document.write( "THe following is what I have tried to complete but am doing something totally wrong. Can you please help.\r<BR>\n" );
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document.write( "-16t^2+800t=3200<BR>\n" );
document.write( "(-16t)^2+800t=3200<BR>\n" );
document.write( "(-16t)(-16t)+800t=3200<BR>\n" );
document.write( "256-16t-16t+2t+800t=3200<BR>\n" );
document.write( "256+2t+800t=3200<BR>\n" );
document.write( "256-256+2t=800t=3200+256<BR>\n" );
document.write( "2t+800t=3456\r<BR>\n" );
document.write( "\n" );
document.write( "Can you please walk me through this and tell me where I went totally wrong. \r<BR>\n" );
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document.write( "Thanks so much!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82026 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your height function is a quadratic equation. You have to use the quadratic formula or factoring to solve it. <BR>\n" );
document.write( "a) Find t when h=3200<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2B800t=3200 ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2B800t=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B800t=3200 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B800t=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B800t-3200=0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B800t-3200=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3200 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-50t%2B200=0 ALIGN=MIDDLE  ALT=\"t%5E2-50t%2B200=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by (-16). <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"t=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Quadratic formula.<BR>\n" );
document.write( "where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-50 ALIGN=MIDDLE  ALT=\"b=-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=200 ALIGN=MIDDLE  ALT=\"c=200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+%2850+%2B-+sqrt%28+50%5E2-4%2A1%2A200+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"t=+%2850+%2B-+sqrt%28+50%5E2-4%2A1%2A200+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+%2850+%2B-+sqrt%28+2500-800+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"t=+%2850+%2B-+sqrt%28+2500-800+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+%2850+%2B-+sqrt%28+1700+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"t=+%2850+%2B-+sqrt%28+1700+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+%2850+%2B-+41.23%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"t=+%2850+%2B-+41.23%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "There are two answers.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+%2850+%2B+41.23%29%2F%282%29=+45.62 ALIGN=MIDDLE  ALT=\"t=+%2850+%2B+41.23%29%2F%282%29=+45.62\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=+%2850+-+41.23%29%2F%282%29=+4.39 ALIGN=MIDDLE  ALT=\"t=+%2850+-+41.23%29%2F%282%29=+4.39\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The rocket starts at zero feet climbs to 3200 and beyond. <BR>\n" );
document.write( "Then it reaches a maximum height and starts to descend. <BR>\n" );
document.write( "The first time it is at 3200 feet, 4.39 seconds, is before the rocket has reached its maximum height. <BR>\n" );
document.write( "The second time it is at 3200 feet, 45.62 seconds, is after it reached the maximum. <BR>\n" );
document.write( "a.) t=4.39 seconds<BR>\n" );
document.write( "Check the answer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2%2B800t=3200 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B800t=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%284.39%29%5E2%2B800%284.39%29=3200 ALIGN=MIDDLE  ALT=\"-16%284.39%29%5E2%2B800%284.39%29=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16%2819.27%29%2B3512=3200 ALIGN=MIDDLE  ALT=\"-16%2819.27%29%2B3512=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-308.3%2B3512=3200 ALIGN=MIDDLE  ALT=\"-308.3%2B3512=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-308.3%2B3512=3200 ALIGN=MIDDLE  ALT=\"-308.3%2B3512=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3203.7=3200 ALIGN=MIDDLE  ALT=\"3203.7=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Close enough. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+50%2C+-1000%2C+11000%2C+-16x%5E2%2B800x%2C3200%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+50%2C+-1000%2C+11000%2C+-16x%5E2%2B800x%2C3200%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b.) We can find the maximum two ways. <BR>\n" );
document.write( "The equation is a parabola and we have two points at the same height. <BR>\n" );
document.write( "The average of the times (4.39 and 45.62) will give us the time when the parabola has its maximum. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Ba%5D=%284.39%2B45.62%29%2F2 ALIGN=MIDDLE  ALT=\"t%5Ba%5D=%284.39%2B45.62%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Ba%5D=25.0 ALIGN=MIDDLE  ALT=\"t%5Ba%5D=25.0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2B800t=3200 ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2B800t=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16%2825%29%5E2%2B800%2825%29 ALIGN=MIDDLE  ALT=\"h=-16%2825%29%5E2%2B800%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16%28625%29%2B800%2825%29 ALIGN=MIDDLE  ALT=\"h=-16%28625%29%2B800%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-10000%2B20000 ALIGN=MIDDLE  ALT=\"h=-10000%2B20000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=10000 ALIGN=MIDDLE  ALT=\"h=10000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The other way is to take the derivative of the height function wrt time and set it to zero to find minima/maxima. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2B800t=3200 ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2B800t=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dh%2Fdt=-32t%2B800 ALIGN=MIDDLE  ALT=\"dh%2Fdt=-32t%2B800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32t%2B800=0 ALIGN=MIDDLE  ALT=\"-32t%2B800=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32t=-800 ALIGN=MIDDLE  ALT=\"-32t=-800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=25 ALIGN=MIDDLE  ALT=\"t=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As before h(25)=10000 feet. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );