document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856050>Question 856050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The parabolic arch in the concrete bridge in<BR>\n" );
document.write( "the figure must have a clearance of 50 feet above the water<BR>\n" );
document.write( "and span a distance of 200 feet. Find the equation of the<BR>\n" );
document.write( "parabola after inserting a coordinate system with the origin<BR>\n" );
document.write( "at the vertex of the parabola and the verticaly axis (point-ing upward) along the axis of the parabola.\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 #515732 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=515732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The parabolic arch in the concrete bridge in the figure must have a clearance of 50 feet above the water and span a distance of 200 feet.<BR>\n" );
document.write( " Find the equation of the parabola after inserting a coordinate system with the origin at the vertex of the parabola and the vertical axis (pointing upward) along the axis of the parabola.<BR>\n" );
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document.write( "from the description, the x intercepts are -100 and +100 and y intercept +50<BR>\n" );
document.write( "Using the form ax^2 + bx + c = y, c = 50, b will cancel,<BR>\n" );
document.write( "two equations for coordinates: x=100, y=0 and x=-100, y=0<BR>\n" );
document.write( "100^2a + 100b + 50 = 0<BR>\n" );
document.write( "-100^2a - 100 + 50 = 0<BR>\n" );
document.write( "which is<BR>\n" );
document.write( "10000a + 100b + 50 = 0<BR>\n" );
document.write( "10000a - 100b + 50 = 0<BR>\n" );
document.write( "----------------------- adding eliminates b, find a<BR>\n" );
document.write( "20000a + 100 = 0<BR>\n" );
document.write( "20000a = -100<BR>\n" );
document.write( "a = -100/20000<BR>\n" );
document.write( "a = -.005<BR>\n" );
document.write( "the equation: y = -.005x^2 + 50, 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+-125%2C+125%2C+-10%2C+60%2C+-.005x%5E2%2B50%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-125%2C+125%2C+-10%2C+60%2C+-.005x%5E2%2B50%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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