document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=873017>Question 873017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bridge is built in the shape of a parabolic arch. The beidge has a span of 120 feet and a maximum height of 25 feet. If the vertex of the parabola is located at (0,0), find the height of the arch 50 feet from the center. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #526639 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=526639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A bridge is built in the shape of a parabolic arch.<BR>\n" );
document.write( " The beidge has a span of 120 feet and a maximum height of 25 feet.<BR>\n" );
document.write( " If the vertex of the parabola is located at (0,0), find the height of the arch 50 feet from the center.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "First find the equation for the parabola, using the ax^2 + bx + c = y<BR>\n" );
document.write( "It crosses the y axis at the origin so we can ignore c<BR>\n" );
document.write( "A 120 ft span, +/-60 on the graph<BR>\n" );
document.write( "Find the equation for each pair<BR>\n" );
document.write( "x=-60, y =-25<BR>\n" );
document.write( "-60^2a - 60b = -25<BR>\n" );
document.write( "3600a - 60b = -25<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=+60, y =-25<BR>\n" );
document.write( "3600a + 60b = -25, add to the 1st equation<BR>\n" );
document.write( "3600a - 60b = -25<BR>\n" );
document.write( "-------------------Adding eliminates b find a<BR>\n" );
document.write( "7200a = -50<BR>\n" );
document.write( "a = -50/7200<BR>\n" );
document.write( "a = -.00694<BR>\n" );
document.write( ";<BR>\n" );
document.write( "We know b is 0 because the vertex is at the origin<BR>\n" );
document.write( "a simple equation<BR>\n" );
document.write( "y = -.00694x^2<BR>\n" );
document.write( "looks like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-80%2C+80%2C+-30%2C+10%2C+-.00694x%5E2%2C+-25%2C+-17.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-80%2C+80%2C+-30%2C+10%2C+-.00694x%5E2%2C+-25%2C+-17.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Surface is green<BR>\n" );
document.write( ":<BR>\n" );
document.write( "find the height of the arch 50 feet from the center.<BR>\n" );
document.write( "x=50<BR>\n" );
document.write( "-.00694(50^2) = -17.5, height will be 25-17.5 = 7.5m above the surface (purple) </SPAN>\n" );
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