document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100161>Question 1100161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suspension Bridge. \r<BR>\n" );
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document.write( "If one parabolic segment of a suspension bridge is 400 feet and if the cables at the vertex are suspended 10 feet above the bridge, whereas the height of the cables 200 feet from the vertex reaches 50 feet, find the equation of the parabolic path of the suspension cables.\r<BR>\n" );
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document.write( "Enter the equation in standard form.\r<BR>\n" );
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document.write( "The equation of the parabolic path of the suspension cables is what? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714670 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=714670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suspension Bridge. <BR>\n" );
document.write( " If one parabolic segment of a suspension bridge is 400 feet and<BR>\n" );
document.write( " if the cables at the vertex are suspended 10 feet above the bridge,<BR>\n" );
document.write( " whereas the height of the cables 200 feet from the vertex reaches 50 feet,<BR>\n" );
document.write( " find the equation of the parabolic path of the suspension cables. <BR>\n" );
document.write( " Enter the equation in standard form. <BR>\n" );
document.write( "Assuming the left side of the bridge is at the origin<BR>\n" );
document.write( "from the information we can create the following pairs<BR>\n" );
document.write( "0,50; 200,10; 400,50. Form equations in the form ax^2 + bx + c = y<BR>\n" );
document.write( "The first pair 0,50 tells us that  c=50<BR>\n" );
document.write( "200,10<BR>\n" );
document.write( "(200^2)a + 200b + 50 = 10<BR>\n" );
document.write( "40000a + 200b = 10 - 50<BR>\n" );
document.write( "40000a + 200b = -40<BR>\n" );
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document.write( "400,50<BR>\n" );
document.write( "(400^2)a + 400b + 50 = 50<BR>\n" );
document.write( "160000a + 400b = 0<BR>\n" );
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document.write( "Use elimination with these two equations, multiply the firs eq by 2<BR>\n" );
document.write( "160000a + 400b = 0<BR>\n" );
document.write( "80000a + 400b = -80<BR>\n" );
document.write( "------------------- subtraction eliminates b, find a<BR>\n" );
document.write( "80000a = 80<BR>\n" );
document.write( "a = 80/80000<BR>\n" );
document.write( "a = .001<BR>\n" );
document.write( "find b using the first original equation<BR>\n" );
document.write( "40000(.001) + 200b = -40<BR>\n" );
document.write( "40 + 200b = -40<BR>\n" );
document.write( "200b = -40 - 40<BR>\n" );
document.write( "b = -80/200<BR>\n" );
document.write( "b = -.4<BR>\n" );
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document.write( "The equation: y = .001x^2 - .4x + 50 <BR>\n" );
document.write( "Graphically, green is 50 ft, blue is 10 ft<BR>\n" );
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document.write( " </SPAN>\n" );
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