document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204029>Question 1204029</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arch is in the shape of a parabola. It has a span of 240 feet and a maximum height of 30 feet.\r<BR>\n" );
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document.write( "a. Find the equation of the parabola (assuming the origin is halfway between the arch's feet).\r<BR>\n" );
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document.write( "b. Determine the height of the arch 107 feet from the center.  </SPAN>\n" );
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document.write( "With the origin halfway between the arch's feet and a maximum height of 30 feet, the vertex of the parabola is (0,30); the equation of the parabola is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-ax%5E2%2B30 ALIGN=MIDDLE  ALT=\"y=-ax%5E2%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "With a distance of 240 feet between the arch's feet, two points on the parabola are (120,0) and (-120,0).  Use either of those two points to find the coefficient a.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-a%28120%29%5E2%2B30 ALIGN=MIDDLE  ALT=\"0=-a%28120%29%5E2%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14400a=30 ALIGN=MIDDLE  ALT=\"14400a=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=30%2F14400=1%2F480 ALIGN=MIDDLE  ALT=\"a=30%2F14400=1%2F480\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER a: The equation of the parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F480%29x%5E2%2B30 ALIGN=MIDDLE  ALT=\"y=-%281%2F480%29x%5E2%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Find the height of the arch 107 feet from the center by finding y when x is 107:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F480%29%28107%5E2%29%2B30 ALIGN=MIDDLE  ALT=\"-%281%2F480%29%28107%5E2%29%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.148 feet to 3 decimal places<br><BR>\n" );
document.write( "ANSWER b: about 6.148 feet<br><BR>\n" );
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