document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922970>Question 922970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9) Bart Simpson is sitting in a treehouse and fires a rock into the air with his (in)famous slingshot.  While in flight, the rock’s distance above the ground is a quadratic function.  At times 1,2, and 3 seconds after being fired, the rock is 68, 96, and 114 feet above the ground respectively.<BR>\n" );
document.write( "&#8203;a) Write the quadratic equation describing the rocks height as a function of time since it was fired.<BR>\n" );
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document.write( "&#8203;b) What is the highest the rock will ever be above the ground?<BR>\n" );
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document.write( "&#8203;c) How long after being fired with the rock hit the ground (assuming Bart missed Homer, who he was aiming at)<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 #559817 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=559817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given points ( 1,68 ), ( 2,96 ), ( 3,114 )<BR>\n" );
document.write( "The general fom is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+-a%2At%5E2+%2B+b%2At+%2B+c+ ALIGN=MIDDLE  ALT=\"+h+=+-a%2At%5E2+%2B+b%2At+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+68+=+-a+%2B+b+%2B+c+ ALIGN=MIDDLE  ALT=\"+68+=+-a+%2B+b+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+96+=+-4a+%2B+2b+%2B+c+ ALIGN=MIDDLE  ALT=\"+96+=+-4a+%2B+2b+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+114+=+-9a+%2B+3b+%2B+c+ ALIGN=MIDDLE  ALT=\"+114+=+-9a+%2B+3b+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( I know the 1st term has to be negative, since that <BR>\n" );
document.write( "is the term that accounts for the downward pull of gravity )<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "subtract (2) from (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+136+=+-2a+%2B+2b+%2B+2c+ ALIGN=MIDDLE  ALT=\"+136+=+-2a+%2B+2b+%2B+2c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-96+=+4a+-+2b+-+c+ ALIGN=MIDDLE  ALT=\"+-96+=+4a+-+2b+-+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+=+2a+%2B+c+ ALIGN=MIDDLE  ALT=\"+40+=+2a+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Now subtract (3) from (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+96+=+-4a+%2B+2b+%2B+c+ ALIGN=MIDDLE  ALT=\"+96+=+-4a+%2B+2b+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-114+=+9a+-+3b+-+c+ ALIGN=MIDDLE  ALT=\"+-114+=+9a+-+3b+-+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-18+=+5a+-+b+ ALIGN=MIDDLE  ALT=\"+-18+=+5a+-+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "From these, I get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+40+-+2a+ ALIGN=MIDDLE  ALT=\"+c+=+40+-+2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+18+%2B+5a+ ALIGN=MIDDLE  ALT=\"+b+=+18+%2B+5a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "plug these into (1), (2), or (3)<BR>\n" );
document.write( "Find c, b, then a<BR>\n" );
document.write( "I have to run<BR>\n" );
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