document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826452>Question 826452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Okay, I am stuck with Paul's trucking company which hauls oversized loads. The truck travels through a tunnel with a wide opening in the shape of a parabola that is 12 meters wide and and 6 meters high.\r<BR>\n" );
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document.write( "How do I find a function, T(x), for the shape of the tunnel. I am also supposed to draw it but it would be a huge favor if I get a walk-in through this and that won't be much of a work if I get that far.\r<BR>\n" );
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document.write( "I appreciate the help in advance, and I look forward to get a reply soon. Thanks :)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #498084 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=498084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The truck travels through a tunnel with a wide opening in the shape of a parabola that is 12 meters wide and and 6 meters high.<BR>\n" );
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document.write( "using the form ax^2 + bx + c = y<BR>\n" );
document.write( "Let's have the parabola have the axis of symmetry at 0, then c = 6<BR>\n" );
document.write( "and the x intercepts will be -6 and +6 (12 m apart)<BR>\n" );
document.write( "write an equation for x = 6, y = 0 and for x = -6, y = 0<BR>\n" );
document.write( "36a + 6b + 6 = 0<BR>\n" );
document.write( "36a - 6b + 6 = 0<BR>\n" );
document.write( "-----------------adding eliminates b, find a<BR>\n" );
document.write( "72a + 12 = 0<BR>\n" );
document.write( "72a = -12<BR>\n" );
document.write( "a = -12/72<BR>\n" );
document.write( "a = -.167<BR>\n" );
document.write( "The middle term cancels so we can write the equation<BR>\n" );
document.write( "T(x) = -.167x^2 + 6<BR>\n" );
document.write( "y = -.167x^2 + 6, graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+10%2C+-3%2C+10%2C-.167x%5E2+%2B+6%2C+3.3+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+10%2C+-3%2C+10%2C-.167x%5E2+%2B+6%2C+3.3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "note that it is 12m wide and 6 m high<BR>\n" );
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document.write( "You can create a table using x and finding y to determine what the height the<BR>\n" );
document.write( "truck can be if you know the width of the truck<BR>\n" );
document.write( "For example if the truck were 8 ft wide, (x = +4, -4), then<BR>\n" );
document.write( "-.167(4^2) + 6 = 3.3 meter, load height has to be less than 3.3 meters (green line)  </SPAN>\n" );
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