document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035950>Question 1035950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The maximum height of the arch is 21feet and the width of the roadway, including shoulder lanes, is 42 feet. At the edge of the left shoulder lane, the height of the arch is 15.4 feet. Determine the width of the arch to the nearest tenth of a foot.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650759 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=650759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5Bv%5D+=+21+ ALIGN=MIDDLE  ALT=\"+h%5Bv%5D+=+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
document.write( "Make the arch a parabola the vertex of which is<BR>\n" );
document.write( "above the center of the roadway. So the vertex is at:<BR>\n" );
document.write( "( 0, 21 )<BR>\n" );
document.write( "The points on the arch at the edges of the roadway are:<BR>\n" );
document.write( "( 42, 15.4 ) <BR>\n" );
document.write( "( -42, 15.4 )<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Let the form of the parabola be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+h%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <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;\" > at the center, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+21+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21+=+a%2A0%5E2+%2B+b%2A0+%2B+c+ ALIGN=MIDDLE  ALT=\"+21+=+a%2A0%5E2+%2B+b%2A0+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+21+ ALIGN=MIDDLE  ALT=\"+c+=+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The formula for the x-value of the vertex is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+0+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+0+ ALIGN=MIDDLE  ALT=\"+b+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So far I have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+=+a%2Ax%5E2+%2B+21+ ALIGN=MIDDLE  ALT=\"+h%28x%29+=+a%2Ax%5E2+%2B+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Plug in point ( 42, 15.4 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%2842%29+=+a%2A%28+42+%29%5E2+%2B+21+ ALIGN=MIDDLE  ALT=\"+h%2842%29+=+a%2A%28+42+%29%5E2+%2B+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%2842%29+=+1764a+%2B+21+ ALIGN=MIDDLE  ALT=\"+h%2842%29+=+1764a+%2B+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%2842%29+=+15.4+ ALIGN=MIDDLE  ALT=\"+h%2842%29+=+15.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15.4+=+1764a+%2B+21+ ALIGN=MIDDLE  ALT=\"+15.4+=+1764a+%2B+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-5.6%2F1764+ ALIGN=MIDDLE  ALT=\"+a+=+-5.6%2F1764+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-.0031746+ ALIGN=MIDDLE  ALT=\"+a+=+-.0031746+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Plugging in ( -42, 15.4 ) gives the same result<BR>\n" );
document.write( "The equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+=+-.0031746x%5E2+%2B+21+ ALIGN=MIDDLE  ALT=\"+h%28x%29+=+-.0031746x%5E2+%2B+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "To find the end points of the arch, set<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28x%29+=+0+ ALIGN=MIDDLE  ALT=\"+h%28x%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-.0031746x%5E2+%2B+21+ ALIGN=MIDDLE  ALT=\"+0+=+-.0031746x%5E2+%2B+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.0031746x%5E2+=+21+ ALIGN=MIDDLE  ALT=\"+.0031746x%5E2+=+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+21%2F.0031746+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+21%2F.0031746+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+6615.007+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+6615.007+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+81.3327+ ALIGN=MIDDLE  ALT=\"+x+=+81.3327+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, also:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-81.3327+ ALIGN=MIDDLE  ALT=\"+x+=+-81.3327+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A81.3327+=+162.6654+ ALIGN=MIDDLE  ALT=\"+2%2A81.3327+=+162.6654+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "The width of the arch is 162.7 ft<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+500%2C+-100%2C+100%2C+-5%2C+30%2C+-+.0031746x%5E2+%2B+21+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+500%2C+-100%2C+100%2C+-5%2C+30%2C+-+.0031746x%5E2+%2B+21+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );