document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=517795>Question 517795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown straight up with an initial velocity of 80 feet per second from the top of a building 23 feet tall.  It's height h (in feet) above the ground t seconds after the ball is thrown is given by h = -16t^2 + 80t + 23.  When will the ball be 119 feet above the ground for the first time?\r<BR>\n" );
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document.write( "*** ^2 stands for squared or to the second power *** </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344937 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=344937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ball will probably be 119' above the ground twice:<BR>\n" );
document.write( "once going up and again coming down.<BR>\n" );
document.write( "Just pick the smallest value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that will<BR>\n" );
document.write( "be going up.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+-16t%5E2+%2B+80t+%2B+23+ ALIGN=MIDDLE  ALT=\"+h+=+-16t%5E2+%2B+80t+%2B+23+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+119+=+-16t%5E2+%2B+80t+%2B+23+ ALIGN=MIDDLE  ALT=\"+119+=+-16t%5E2+%2B+80t+%2B+23+\"   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+%2B+80t+%2B+23+-+119+=+0+ ALIGN=MIDDLE  ALT=\"+-16t%5E2+%2B+80t+%2B+23+-+119+=+0+\"   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+%2B+80t+-+96+=+0+ ALIGN=MIDDLE  ALT=\"+-16t%5E2+%2B+80t+-+96+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-t%5E2+%2B+5t+-+6+=+0+ ALIGN=MIDDLE  ALT=\"+-t%5E2+%2B+5t+-+6+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<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;\" > <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+=+5+ ALIGN=MIDDLE  ALT=\"+b+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-6+ ALIGN=MIDDLE  ALT=\"+c+=+-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A%28-1%29%2A%28-6%29+%29%29%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A%28-1%29%2A%28-6%29+%29%29%2F%282%2A%28-1%29%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+=+%28-5+%2B-+sqrt%28+25+-+24+%29%29%2F%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-5+%2B-+sqrt%28+25+-+24+%29%29%2F%28-2%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+=+%28+-5+%2B+1+%29+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-5+%2B+1+%29+%2F+%28-2%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+=+2+ ALIGN=MIDDLE  ALT=\"+t+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, also,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-5+-+1%29+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-5+-+1%29+%2F+%28-2%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+=+3+ ALIGN=MIDDLE  ALT=\"+t+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2 sec from when the ball is thrown, the<BR>\n" );
document.write( "height will be 119' above ground for the first time.<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+119+=+-16t%5E2+%2B+80t+%2B+23+ ALIGN=MIDDLE  ALT=\"+119+=+-16t%5E2+%2B+80t+%2B+23+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+119+=-16%2A4+%2B+80%2A2+%2B+23+ ALIGN=MIDDLE  ALT=\"+119+=-16%2A4+%2B+80%2A2+%2B+23+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+119+=+-64+%2B+160+%2B+23+ ALIGN=MIDDLE  ALT=\"+119+=+-64+%2B+160+%2B+23+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+119+=+96+%2B+23+ ALIGN=MIDDLE  ALT=\"+119+=+96+%2B+23+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+119+=+119+ ALIGN=MIDDLE  ALT=\"+119+=+119+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Here's a plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-1%2C+6%2C+-10%2C+130%2C+-16x%5E2+%2B+80x+%2B+23+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-1%2C+6%2C+-10%2C+130%2C+-16x%5E2+%2B+80x+%2B+23+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );