document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=271750>Question 271750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The B Bridge connects SI and NY to NJ.  It has an arch in the sharpe of a parabola that opens downward.  Write an equation of a parabola to model the arch, assuming that the origin is at the surface of the water, beneath the vertex of the arch.  end to end bridge if 1675 ft; base to top is 325 ft.  \r<BR>\n" );
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document.write( "This is in chapter 8, pg 424 problem 43 of Glencoe Mathematics, algebra 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199224 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=199224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The B Bridge connects SI and NY to NJ. It has an arch in the shape of a parabola that opens downward. <BR>\n" );
document.write( "Write an equation of a parabola to model the arch, assuming that the origin is at the surface of the water,<BR>\n" );
document.write( " beneath the vertex of the arch. end to end bridge if 1675 ft; base to top is 325<BR>\n" );
document.write( " ft.<BR>\n" );
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document.write( "We can create a quadratic equation using the form: ax^2 + bx + c = y<BR>\n" );
document.write( "c is 0, so we can just solve for a and b, using elimination:<BR>\n" );
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document.write( "x = 1675, y = 324 (the vertex)<BR>\n" );
document.write( "1675^2a + 1675b = 325<BR>\n" );
document.write( "2805625a + 1675b = 325<BR>\n" );
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document.write( "x = 3350, y = 0 (opposite end of the bridge where the arch at the water level)<BR>\n" );
document.write( "3350^2a + 3350b = 0<BR>\n" );
document.write( "11222500a + 3350b = 0<BR>\n" );
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document.write( "Multiply the 1st equation by 2, subtract the 2nd equation<BR>\n" );
document.write( "561125a + 3350b = 650<BR>\n" );
document.write( "11222500a + 3350b = 0<BR>\n" );
document.write( "----------------------subtraction eliminates b, find a<BR>\n" );
document.write( "-5611250a = 650<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=650%2F%28-5611250%29 ALIGN=MIDDLE  ALT=\"650%2F%28-5611250%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -.0001158<BR>\n" );
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document.write( "Find b<BR>\n" );
document.write( "-.0001158(1675^2) + 1675b = 325<BR>\n" );
document.write( "-324.89 + 1675b = 325<BR>\n" );
document.write( "1650b = 325 + 324.89<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=649.89%2F1675 ALIGN=MIDDLE  ALT=\"649.89%2F1675\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = .388<BR>\n" );
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document.write( "the equation of the arch y = -.0001158x^2 + .388x<BR>\n" );
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document.write( "A graph will illustrate this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1000%2C+4000%2C+-100%2C+400%2C+-.00011158x%5E2%2B.388x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-1000%2C+4000%2C+-100%2C+400%2C+-.00011158x%5E2%2B.388x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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