document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152047>Question 152047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circus performer is juggling clubs while standing on stilts. He releases a club from a point 8ft above the ground with the initial vertical velocity of 10 ft per second. \r<BR>\n" );
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document.write( "The vertical motion mode is h = -16t2(It's t to the second power) + vt + s where he is the height of an object in feet, t is the time seconds, v is the initial vertical velocity in feet per second, and s is the initial height in feet. \r<BR>\n" );
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document.write( "a) Write an equation in function notation that models the height (in feet) of the club as a function of time (in seconds).\r<BR>\n" );
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document.write( "b) Make a table of the time in the air and the heights of the club from 0.1 seconds to 1.5 seconds.\r<BR>\n" );
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document.write( "c) Graph the function and label the vertex.\r<BR>\n" );
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document.write( "d) How long after the club is released does the club reach its maximum height?  What was the maximum height?\r<BR>\n" );
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document.write( "e) How long after the club is released will it return to the ground?  How do you know this?\r<BR>\n" );
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document.write( "Thanks so much for your help!!!!<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 #111774 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=111774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16t%5E2+%2B+v%5B0%5Dt+%2B+s%5B0%5D ALIGN=MIDDLE  ALT=\"h+=+-16t%5E2+%2B+v%5B0%5Dt+%2B+s%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "You are told the initial velocity is 10 feet/sec so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D+=+10 ALIGN=MIDDLE  ALT=\"v%5B0%5D+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You are told the initial position is 8 feet above the grouns. so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B0%5D+=+10 ALIGN=MIDDLE  ALT=\"s%5B0%5D+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute that info into the equation to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-16t%5E2+%2B+10t+%2B+8+ ALIGN=MIDDLE  ALT=\"h+=+-16t%5E2+%2B+10t+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Plug in values for t from 0.1 through 1.5 and solve for h. You'll need to grind that out by hand., Just pick a few values for t and solve for h using the eqaution we just made.\r<BR>\n" );
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document.write( "graph the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C+-1%2C3%2C+-1%2C+11%2C+-16x%5E2+%2B10x+%2B8%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C+-1%2C3%2C+-1%2C+11%2C+-16x%5E2+%2B10x+%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "height is the y axis, time is the x axis.\r<BR>\n" );
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document.write( "To find the max height, look at the plot. Mark that point and then drop down to find the time and across to find the height\r<BR>\n" );
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document.write( "To find when it hits the round, set h = 0 and solve for t. Or look at the plot and find the time when the graph touches the x axis  </SPAN>\n" );
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