document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=733982>Question 733982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Part of Sydney Harbor Bridge in Sydney,Australia can be modeled by a parabolic<BR>\n" );
document.write( "arch. If the arch would pass through the points (0,23) (-5,2), (4,-40),write the<BR>\n" );
document.write( "equation of the parabola to model the arch. \r<BR>\n" );
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document.write( "Please help me solve this  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448673 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=448673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Part of Sydney Harbor Bridge in Sydney,Australia can be modeled by a parabolic<BR>\n" );
document.write( "arch.<BR>\n" );
document.write( "If the arch would pass through the points (0,23) (-5,2), (4,-40), write the<BR>\n" );
document.write( "equation of the parabola to model the arch. <BR>\n" );
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document.write( "Using the form, ax^2 + bx + c = y, find a, b, c<BR>\n" );
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document.write( "The first pair, 0,23; tells us that c = 23, find a and b with remaining pairs<BR>\n" );
document.write( "-5,2<BR>\n" );
document.write( "-5^2a - 5b + 23 = 2<BR>\n" );
document.write( "25a - 5x = 2 - 23<BR>\n" );
document.write( "25a - 5b = -21<BR>\n" );
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document.write( "4,-40<BR>\n" );
document.write( "4^2a + 4b + 23 = -40<BR>\n" );
document.write( "16a + 4b = -40 - 23<BR>\n" );
document.write( "16a + 4b = -63<BR>\n" );
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document.write( "multiply the 1st equation by 4, and the 2nd equation by 5, and add them<BR>\n" );
document.write( "100a - 20b = -84<BR>\n" );
document.write( "80a + 20b = -315<BR>\n" );
document.write( "------------------addition eliminates b, find a<BR>\n" );
document.write( "180a = -399<BR>\n" );
document.write( "a = -399/180<BR>\n" );
document.write( "a = -2.2167<BR>\n" );
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document.write( "Find b using the 16a + 4b = -63<BR>\n" );
document.write( "16(-2.21676) + 4b = -63<BR>\n" );
document.write( "-35.467 + 4b = -63<BR>\n" );
document.write( "4b = -63 + 35.467<BR>\n" );
document.write( "4b = -27.533<BR>\n" );
document.write( "b = -27.533/4<BR>\n" );
document.write( "b = -6.883<BR>\n" );
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document.write( "The equation: y = -2.2167x^2 - 6.883x + 23; for the parabolic arch<BR>\n" );
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document.write( "Graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-8%2C+5%2C+-50%2C+50%2C+-2.2167x%5E2+-+6.883x+%2B+23+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-8%2C+5%2C+-50%2C+50%2C+-2.2167x%5E2+-+6.883x+%2B+23+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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