document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1015369>Question 1015369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A water ballon is launched from a launcher, up into the air from a platform. The height of the balloon in feet, is a function of the time in seconds since it was launched: f(t)= 16t^2+V0t+H0 where V0 represents the initial upward velocity of the launch, and H0 represents the height of balloon right when it is launched. Lorenzo launches his water balloon with an initial upward velocity of 80 ft per second. The initial height of the water balloon is 5ft off the ground what is the maximum height of the water balloon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #631742 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=631742\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are missing a minus sign in front of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2 ALIGN=MIDDLE  ALT=\"16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28f%28t%29=-16t%5E2%2BV%5B0%5Dt%2BH%5B0%5D%2CV%5B0%5D=80%2CH%5B0%5D=5%29 ALIGN=MIDDLE  ALT=\"system%28f%28t%29=-16t%5E2%2BV%5B0%5Dt%2BH%5B0%5D%2CV%5B0%5D=80%2CH%5B0%5D=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29=-16t%5E2%2B80t%2B5 ALIGN=MIDDLE  ALT=\"f%28t%29=-16t%5E2%2B80t%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "JUST USING ALGEBRA:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29=-%284t%29%5E2%2B2%2A%284t%29%2A10-10%5E2%2B5%2B10%5E2=-%28%284t%29%5E2-2%2A%284t%29%2A10%2B10%5E2%29%2B5%2B100=-%284t-10%29%5E2%2B105%3C=105 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "APPLYING A FORMULA:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29=-16t%5E2%2B80t%2B5 ALIGN=MIDDLE  ALT=\"f%28t%29=-16t%5E2%2B80t%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a quadratic function.<BR>\n" );
document.write( "A quadratic function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C0 ALIGN=MIDDLE  ALT=\"a%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a maximum at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so, in this case, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=t%2Ca=-16%2Cb=80%2Cc=5%29 ALIGN=MIDDLE  ALT=\"system%28x=t%2Ca=-16%2Cb=80%2Cc=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the maximum happens at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-80%29%2F%282%28-16%29%29=%28-80%29%2F%28-32%29=2.5 ALIGN=MIDDLE  ALT=\"t=%28-80%29%2F%282%28-16%29%29=%28-80%29%2F%28-32%29=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The maximum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282.5%29=-16%2A2.5%5E2%2B80%2A2.5%2B5=-16%2A6.25%2B200%2B5-100%2B200%2B5=105 ALIGN=MIDDLE  ALT=\"f%282.5%29=-16%2A2.5%5E2%2B80%2A2.5%2B5=-16%2A6.25%2B200%2B5-100%2B200%2B5=105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So, the maximum height of the water balloon is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28105feet%29 ALIGN=MIDDLE  ALT=\"highlight%28105feet%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " </SPAN>\n" );
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