document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142336>Question 1142336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a bridge cable connecting two towers forms a parabola. the lowest point is 55m about the waters surface. the origin is at the point where the cable is attached to the southern tower 75m above the waters surface. the other end is attached to the northern tower 120 m away, write a quadratic function in standard form </SPAN>\n" );
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document.write( "Alan is right; since you don't say what height the cable attaches to the northern tower, the question as stated can't be solved.<br><BR>\n" );
document.write( "So let's assume the logical thing -- that the cable is connected to both towers the same height above the water.<br><BR>\n" );
document.write( "We are told to use as the origin the point where the cable attaches to the southern tower.  So one point on the parabola is (0,0).<br><BR>\n" );
document.write( "Since the two towers are 120m apart, another point on the parabola is (120,0).<br><BR>\n" );
document.write( "By symmetry, the minimum point on the parabola is halfway between the two towers.  Since the point where the cable attaches to each of the two towers is 75m above the water and the lowest point of the cable is 55m above the water, the minimum point on the parabola (the vertex) is (60,-20).<br><BR>\n" );
document.write( "So a vertex form of the equation of the parabola is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B20+=+a%28x-60%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B20+=+a%28x-60%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To find the value of a, use one of the two other known points on the parabola.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B20+=+a%280-60%29%5E2 ALIGN=MIDDLE  ALT=\"0%2B20+=+a%280-60%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+=+3600a ALIGN=MIDDLE  ALT=\"20+=+3600a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1%2F180 ALIGN=MIDDLE  ALT=\"a+=+1%2F180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In vertex form, the equation of the parabola is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B20+=+%281%2F180%29%28x-60%29%5E2 ALIGN=MIDDLE  ALT=\"y%2B20+=+%281%2F180%29%28x-60%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can convert that to whatever form you need. </SPAN>\n" );
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