document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132760>Question 1132760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arch in the shape of a parabola has height 630ft and width 630ft. How wide is the arch 300 ft up? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749880 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An arch in the shape of a parabola has height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=630ft ALIGN=MIDDLE  ALT=\"630ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > and width <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=630ft ALIGN=MIDDLE  ALT=\"630ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >. How wide is the arch <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300ft ALIGN=MIDDLE  ALT=\"300ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > up? \r<BR>\n" );
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document.write( "The width of the bridge is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=630 ALIGN=MIDDLE  ALT=\"630\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet so the parabola crosses the x-axis with x-coordinates ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=630%2F2 ALIGN=MIDDLE  ALT=\"630%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=315 ALIGN=MIDDLE  ALT=\"315\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> x-intercepts are at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-315 ALIGN=MIDDLE  ALT=\"-315\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=315 ALIGN=MIDDLE  ALT=\"315\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Assume that it stands on the x axis, that it is symmetric with respect to the y-axis, and that it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=630 ALIGN=MIDDLE  ALT=\"630\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet wide at the base and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=630 ALIGN=MIDDLE  ALT=\"630\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet high at the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=center ALIGN=MIDDLE  ALT=\"center\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " Then the maximum height occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, the vertex of the parabola is  =>(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=630 ALIGN=MIDDLE  ALT=\"630\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Since the curve is a parabola which opens downward its equation can be written \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+a%28x-h%29%5E2+%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29+=+a%28x-h%29%5E2+%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=630 ALIGN=MIDDLE  ALT=\"k=630\"   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=f%28x%29+=+a%28x-0%29%5E2+%2B630 ALIGN=MIDDLE  ALT=\"f%28x%29+=+a%28x-0%29%5E2+%2B630\"   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=f%28x%29+=+ax%5E2+%2B630 ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2+%2B630\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x-intercepts are at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-315 ALIGN=MIDDLE  ALT=\"-315\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >), use x-intercept to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   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%28-315%29%5E2+%2B630 ALIGN=MIDDLE  ALT=\"0+=+a%28-315%29%5E2+%2B630\"   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+=99225%2Aa+%2B630 ALIGN=MIDDLE  ALT=\"0+=99225%2Aa+%2B630\"   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=99225+a+=-630 ALIGN=MIDDLE  ALT=\"99225+a+=-630\"   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+=-630%2F99225 ALIGN=MIDDLE  ALT=\"+a+=-630%2F99225\"   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+=-2%2F315 ALIGN=MIDDLE  ALT=\"a+=-2%2F315\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and, equation is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-%282%2F315%29x%5E2+%2B630 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-%282%2F315%29x%5E2+%2B630\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to find how wide is the arch <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300ft ALIGN=MIDDLE  ALT=\"300ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > up, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+300ft ALIGN=MIDDLE  ALT=\"f%28x%29=+300ft\"   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=300+=+-%282%2F315%29x%5E2+%2B630 ALIGN=MIDDLE  ALT=\"300+=+-%282%2F315%29x%5E2+%2B630\"   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=%282%2F315%29x%5E2+=630-300 ALIGN=MIDDLE  ALT=\"%282%2F315%29x%5E2+=630-300\"   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=%282%2F315%29x%5E2+=330 ALIGN=MIDDLE  ALT=\"%282%2F315%29x%5E2+=330\"   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=x%5E2+=330%2F%282%2F315%29 ALIGN=MIDDLE  ALT=\"x%5E2+=330%2F%282%2F315%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=x%5E2+=%28330%2A315%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E2+=%28330%2A315%29%2F2\"   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=x%5E2+=165%2A315 ALIGN=MIDDLE  ALT=\"x%5E2+=165%2A315\"   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=x%5E2+=51975 ALIGN=MIDDLE  ALT=\"x%5E2+=51975\"   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=x+=sqrt%2851975%29 ALIGN=MIDDLE  ALT=\"x+=sqrt%2851975%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=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=227.98 ALIGN=MIDDLE  ALT=\"227.98\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the arch <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300 ALIGN=MIDDLE  ALT=\"300\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft have intercepts at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-227.98 ALIGN=MIDDLE  ALT=\"-227.98\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300 ALIGN=MIDDLE  ALT=\"300\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=227.98 ALIGN=MIDDLE  ALT=\"227.98\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300 ALIGN=MIDDLE  ALT=\"300\"   DISABLED_style= \"max-width:90%; height:auto;\" >), so width will be the distance from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-227.98 ALIGN=MIDDLE  ALT=\"x=-227.98\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=227.98 ALIGN=MIDDLE  ALT=\"x=227.98\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A227.98=455.96 ALIGN=MIDDLE  ALT=\"+2%2A227.98=455.96\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft\r<BR>\n" );
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document.write( "answer: the arch <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300 ALIGN=MIDDLE  ALT=\"300\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft up is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+455.96 ALIGN=MIDDLE  ALT=\"+455.96\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft wide\r<BR>\n" );
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document.write( " </SPAN>\n" );
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