document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199175>Question 199175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem.  <BR>\n" );
document.write( "   A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the equation of the parabola. Then calculate the height of the arch 10, 20 and 40 feet from the center. Provide a sketch representing the situation and be sure it is clearly labled with coordinates. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149648 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the equation of the parabola. Then calculate the height of the arch 10, 20 and 40 feet from the center. Provide a sketch representing the situation and be sure it is clearly labled with coordinates.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C130%2C-10%2C60%2C+locate%2840%2C30%2CVertex%2860%2C25%29%29%2C%0D%0A%0D%0Agraph%28400%2C400%2C-10%2C130%2C-10%2C60%2C%28sqrt%28x%29%2Fsqrt%28x%29%29%2A%28sqrt%28120-x%29%2Fsqrt%28120-x%29%29%2A%28-1%2F144%29%28x-60%29%5E2%2B25%29%2Cline%2860%2C24.8%2C60%2C25.2%29%0D%0A%0D%0A%0D%0A%29%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The equation of the parabola with vertex (h,k) is\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "So the equation of the parabola with vertex (60,25) is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-60%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"y=a%28x-60%29%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since it goes through (0,0) we substitute that in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%280-60%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"0=a%280-60%29%5E2%2B25\"   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%28-60%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"0=a%28-60%29%5E2%2B25\"   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%283600%29%2B25 ALIGN=MIDDLE  ALT=\"0=a%283600%29%2B25\"   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=3600a%2B25 ALIGN=MIDDLE  ALT=\"0=3600a%2B25\"   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=-3600a=25 ALIGN=MIDDLE  ALT=\"-3600a=25\"   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=25%2F%28-3600%29 ALIGN=MIDDLE  ALT=\"a=25%2F%28-3600%29\"   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=-1%2F144 ALIGN=MIDDLE  ALT=\"a=-1%2F144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the equation of the parabola is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F144%29%28x-60%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%28x-60%29%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find the height 10 feet from the center,<BR>\n" );
document.write( "since the center is at 60, 10 feet from the<BR>\n" );
document.write( "center is where x=50 and where x=70<BR>\n" );
document.write( "we can either substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50 ALIGN=MIDDLE  ALT=\"x=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=70 ALIGN=MIDDLE  ALT=\"x=70\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting 50,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F144%29%2850-60%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%2850-60%29%5E2%2B25\"   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=y=%28-1%2F144%29%28-10%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%28-10%29%5E2%2B25\"   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=y=%28-1%2F144%29%28100%29%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%28100%29%2B25\"   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=y=24.3056 ALIGN=MIDDLE  ALT=\"y=24.3056\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet, approximately\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C130%2C-10%2C60%2C+locate%2840%2C30%2CVertex%2860%2C25%29%29%2C%0D%0Aline%2850%2C0%2C50%2C875%2F36%29%2C+line%2870%2C0%2C70%2C875%2F36%29%2C%0D%0Agraph%28400%2C400%2C-10%2C130%2C-10%2C60%2C%28sqrt%28x%29%2Fsqrt%28x%29%29%2A%28sqrt%28120-x%29%2Fsqrt%28120-x%29%29%2A%28-1%2F144%29%28x-60%29%5E2%2B25%29%2Cline%2860%2C24.8%2C60%2C25.2%29%29+%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find the height 20 feet from the center,<BR>\n" );
document.write( "since the center is at 60, 20 feet from the<BR>\n" );
document.write( "center is where x=40 and where x=80<BR>\n" );
document.write( "we can either substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=40 ALIGN=MIDDLE  ALT=\"x=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=80 ALIGN=MIDDLE  ALT=\"x=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting 40,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F144%29%2840-60%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%2840-60%29%5E2%2B25\"   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=y=%28-1%2F144%29%28-20%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%28-20%29%5E2%2B25\"   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=y=%28-1%2F144%29%28400%29%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%28400%29%2B25\"   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=y=22.2222 ALIGN=MIDDLE  ALT=\"y=22.2222\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet, approximately\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C130%2C-10%2C60%2C+locate%2840%2C30%2CVertex%2860%2C25%29%29%2C%0D%0Aline%2840%2C0%2C40%2C200%2F9%29%2C+line%2880%2C0%2C80%2C200%2F9%29%2C+%0D%0Agraph%28400%2C400%2C-10%2C130%2C-10%2C60%2C%28sqrt%28x%29%2Fsqrt%28x%29%29%2A%28sqrt%28120-x%29%2Fsqrt%28120-x%29%29%2A%28-1%2F144%29%28x-60%29%5E2%2B25%29%2Cline%2860%2C24.8%2C60%2C25.2%29%29+%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find the height 40 feet from the center,<BR>\n" );
document.write( "since the center is at 60, 40 feet from the<BR>\n" );
document.write( "center is where x=20 and where x=100<BR>\n" );
document.write( "we can either substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20 ALIGN=MIDDLE  ALT=\"x=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=100 ALIGN=MIDDLE  ALT=\"x=100\"   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=y=%28-1%2F144%29%2820-60%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%2820-60%29%5E2%2B25\"   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=y=%28-1%2F144%29%28-40%29%5E2%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%28-40%29%5E2%2B25\"   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=y=%28-1%2F144%29%281600%29%2B25 ALIGN=MIDDLE  ALT=\"y=%28-1%2F144%29%281600%29%2B25\"   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=y=13.6111 ALIGN=MIDDLE  ALT=\"y=13.6111\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet, approximately\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C130%2C-10%2C60%2C+locate%2840%2C30%2CVertex%2860%2C25%29%29%2C%0D%0Aline%2820%2C0%2C20%2C245%2F18%29%2Cline%28100%2C0%2C100%2C245%2F18%29%2C%0D%0Agraph%28400%2C400%2C-10%2C130%2C-10%2C60%2C%28sqrt%28x%29%2Fsqrt%28x%29%29%2A%28sqrt%28120-x%29%2Fsqrt%28120-x%29%29%2A%28-1%2F144%29%28x-60%29%5E2%2B25%29%2Cline%2860%2C24.8%2C60%2C25.2%29%29+%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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