document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=812162>Question 812162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A goalie kicks a soccer ball with an upward velocity of 65 feet per second, and her foot meets the ball 1 foot off the ground. The quadratic function h=16tsquared + 65t + 1 represents the height of the ball h in feet after t seconds. Approximately how long is the ball in the air? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #489036 by </B><A HREF=/tutors/aboutme.mpl?userid=brysca><B>brysca(112)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=brysca><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=brysca><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=489036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This relates to the physics equation, Y=Yo+Vot+.5at^2<BR>\n" );
document.write( "This equation is not factorable, so there is no other option to use except through the quadratic formula. (I think the problem may have been typed wrong, so I am making the \"a\" value -16 instead of 16.)<BR>\n" );
document.write( "The equation can be re-written as this:<BR>\n" );
document.write( "-16t^2+65t+1=0<BR>\n" );
document.write( "a=-16<BR>\n" );
document.write( "b=65<BR>\n" );
document.write( "c=1<BR>\n" );
document.write( "Now, we use the quadratic formula, which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and plug in the respective variables.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-65+%2B-+sqrt%28+65%5E2-4%2A-16%2A1%29%29%2F%282%2A-16%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-65+%2B-+sqrt%28+65%5E2-4%2A-16%2A1%29%29%2F%282%2A-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This simplifes to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-65+%2B-+sqrt%284289%29%29%2F-32+ ALIGN=MIDDLE  ALT=\"+%28-65+%2B-+sqrt%284289%29%29%2F-32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Nothing can be simplified in the above equation so if you plug in the numbers, your answer should be<BR>\n" );
document.write( "t=-0.0153267912541177, 4.07782679125412 because there's always two answers in quadratics.<BR>\n" );
document.write( "Time obviously cannot be negative so the answer you are left with is t=4.07782679125412.<BR>\n" );
document.write( "Or you can just say t equals about 4 seconds.\r<BR>\n" );
document.write( "\n" );
document.write( "Cheers,<BR>\n" );
document.write( "-Bryan </SPAN>\n" );
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