document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=324138>Question 324138</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bridge uses a parabolic arch to support it as shown in the picture. The bridge is 100 m long and has a maximum height of 75m. \r<BR>\n" );
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document.write( "Determine an algebraic expression, in standard form, that models the shape of the bridge.\r<BR>\n" );
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document.write( "If you must drive 10 m on the bridge before you reach the arch, how high is the bridge above the water below ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #232002 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=232002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is no picture, so I will try to extrapolate.\r<BR>\n" );
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document.write( "Center it at the origin. The parabola representing the bridge arch passes through (50,0) and (-50,0) and has its vertex at (0,75).\r<BR>\n" );
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document.write( "We can use the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > to model the parabola.\r<BR>\n" );
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document.write( "Plug in the given points and solve for a.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%2850-0%29%5E2%2B75 ALIGN=MIDDLE  ALT=\"0=a%2850-0%29%5E2%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%2A2500%2B75 ALIGN=MIDDLE  ALT=\"0=a%2A2500%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-75%2F2500=-3%2F100 ALIGN=MIDDLE  ALT=\"a=-75%2F2500=-3%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the parabola equation is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2F100%2Ax%5E2%2B75 ALIGN=MIDDLE  ALT=\"y=-3%2F100%2Ax%5E2%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find how high it is at a point, simply plug in the corresponding x value.\r<BR>\n" );
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document.write( "i.e. How high is the arch at x=25?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F100%2A%2825%29%5E2%2B75=56.25 ALIGN=MIDDLE  ALT=\"-3%2F100%2A%2825%29%5E2%2B75=56.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > m </SPAN>\n" );
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