document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826459>Question 826459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Okay, so I am stuck with Paul's truck company which hauls oversized loads. The trucks travel through a tunnel with an opening in the shape of a parabola that is 12 meters wide and 6 meters high.\r<BR>\n" );
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document.write( "I am told to find a function, T(x), for the shape of the tunnel...I am also supposed to graph it but I don't think that would be much of a trouble if I get a walk-in thus far.\r<BR>\n" );
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document.write( "I appreciate your help in advance, and I will be looking forward to your reply soon. Thanks a bunch! :)<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 #498085 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=498085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can say that this is a parabola that looks like a bowl<BR>\n" );
document.write( "turned upside down. To simplify, say it is symmetric<BR>\n" );
document.write( "about the origin. That means it intersects the x-axis<BR>\n" );
document.write( "at ( 6,0 ) and ( -6,0 ) The T-intercept is at ( 0,6 ).<BR>\n" );
document.write( "-------------------------------------------<BR>\n" );
document.write( "The general form of the parabola is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T%28x%29+=+-a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+T%28x%29+=+-a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The formula for the vertex is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the vertex is on the y-axis,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+0+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T%28x%29+=+-a%2A0%5E2+%2B+b%2A0+%2B+c+ ALIGN=MIDDLE  ALT=\"+T%28x%29+=+-a%2A0%5E2+%2B+b%2A0+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bv%5D+=+6+ ALIGN=MIDDLE  ALT=\"+y%5Bv%5D+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+=+c+ ALIGN=MIDDLE  ALT=\"+6+=+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "So far, I have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T%28x%29+=+-a%2Ax%5E2+%2B+b%2Ax+%2B+6+ ALIGN=MIDDLE  ALT=\"+T%28x%29+=+-a%2Ax%5E2+%2B+b%2Ax+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug in ( 6,0 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-a%2A6%5E2+%2B+b%2A6+%2B+6+ ALIGN=MIDDLE  ALT=\"+0+=+-a%2A6%5E2+%2B+b%2A6+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-36a+%2B+6b+%2B+6+=+0+ ALIGN=MIDDLE  ALT=\"+-36a+%2B+6b+%2B+6+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6a+%2B+b+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+-6a+%2B+b+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6a+%2B+b+=+-1+ ALIGN=MIDDLE  ALT=\"+-6a+%2B+b+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "also<BR>\n" );
document.write( "Plug in (-6,0 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T%28x%29+=+-a%2A%28-6%29%5E2+%2B+b%2A%28-6%29+%2B+6+ ALIGN=MIDDLE  ALT=\"+T%28x%29+=+-a%2A%28-6%29%5E2+%2B+b%2A%28-6%29+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-36a+-+6b+%2B+6+ ALIGN=MIDDLE  ALT=\"+0+=+-36a+-+6b+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-36a+-+6b+%2B+6+=+0+ ALIGN=MIDDLE  ALT=\"+-36a+-+6b+%2B+6+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6a+-+b+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+-6a+-+b+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6a+-+b+=+-1+ ALIGN=MIDDLE  ALT=\"+-6a+-+b+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add (1) and (2)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6a+%2B+b+=+-1+ ALIGN=MIDDLE  ALT=\"+-6a+%2B+b+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6a+-+b+=+-1+ ALIGN=MIDDLE  ALT=\"+-6a+-+b+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12a+=+-2+ ALIGN=MIDDLE  ALT=\"+-12a+=+-2+\"   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%2F6+ ALIGN=MIDDLE  ALT=\"+a+=+1%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Plug this back in:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6%2A%281%2F6%29+%2B+b+=+-1+ ALIGN=MIDDLE  ALT=\"+-6%2A%281%2F6%29+%2B+b+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1+%2B+b+=+-1+ ALIGN=MIDDLE  ALT=\"+-1+%2B+b+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+0+ ALIGN=MIDDLE  ALT=\"+b+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "So, the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T%28x%29+=+-%281%2F6%29%2Ax%5E2+%2B+6+=+0+ ALIGN=MIDDLE  ALT=\"+T%28x%29+=+-%281%2F6%29%2Ax%5E2+%2B+6+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-8%2C+8%2C+-2%2C+8%2C+-%281%2F6%29%2Ax%5E2+%2B+6+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-8%2C+8%2C+-2%2C+8%2C+-%281%2F6%29%2Ax%5E2+%2B+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );