document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181355>Question 1181355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diagram shows a suspension bridge with a center span of 4200 ft. and a tower height of<BR>\n" );
document.write( "500 ft. with the lowest part of the suspender 10 ft. above the base of the bridge. Write an<BR>\n" );
document.write( "equation to represent the curve of the suspender with h, the tower height from the base of the<BR>\n" );
document.write( "bridge, in ft. as a function of d, the horizontal distance from the center of the bridge, in ft.,<BR>\n" );
document.write( "assuming that the suspender is symmetrical in shape.\r<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 #811297 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The topic you chose was quadratic equations; in the text of your message you only said that the suspender is symmetrical in shape.<br><BR>\n" );
document.write( "A parabola is symmetrical, so forming a quadratic equation from the given information makes sense.<br><BR>\n" );
document.write( "Note, however, that a suspender hanging freely from two towers does NOT form a parabola -- it forms a catenary.  Equations of catenaries are far more complicated than equations of parabolas.<br><BR>\n" );
document.write( "So I will outline a process for finding the equation of a parabola that satisfies the given conditions -- assuming that is what you were asked to do.<br><BR>\n" );
document.write( "The vertex of the parabola is 10 feet above the roadway.  2100 feet either direction from the center of the span, the parabola passes through a point 500 feet above the roadway, which is 490 feet above the vertex.<br><BR>\n" );
document.write( "The equation for the height of the suspender above the roadway, as a function of the distance from the center of the bridge, is then rather simple in vertex form: y = ax^2+10.<br><BR>\n" );
document.write( "Use the point (2100,490) to find the value of the constant a.<br><BR>\n" );
document.write( "I leave it to you to do that little bit of work to finish finding the equation.<br><BR>\n" );
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