document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091906>Question 1091906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A parabolic arch is constructed which is 8 ft wide at the base and 9 feet tall. Find the height of the arch exactly 1 foot in from the base of the arch<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706396 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=706396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>Put the top of the arch (the vertex of the parabola) at the origin.  Then since the parabola opens downward, the equation of the parabola is of the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2 ALIGN=MIDDLE  ALT=\"y+=+ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where a is a negative constant.<br><BR>\n" );
document.write( "If the arch is 8 feet wide and 9 feet high, then the coordinates of the bases of the arch are (-4,-9) and (4,-9).  We can use the coordinates of either of those points to determine the value of the constant a.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9+=+a%284%29%5E2 ALIGN=MIDDLE  ALT=\"-9+=+a%284%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=-9+=+16a ALIGN=MIDDLE  ALT=\"-9+=+16a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-9%2F16 ALIGN=MIDDLE  ALT=\"a+=+-9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the equation of the parabola is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%289%2F16%29x%5E2 ALIGN=MIDDLE  ALT=\"y+=+-%289%2F16%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "One foot from the right base of the arch, the x value is 3; that makes the y value<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%289%2F16%29%283%5E2%29+=+-81%2F16 ALIGN=MIDDLE  ALT=\"-%289%2F16%29%283%5E2%29+=+-81%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The number we want is the height of the arch 1 foot from its base; that is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-81%2F16%29-%28-9%29+=+-81%2F16+%2B+144%2F16+=+63%2F16 ALIGN=MIDDLE  ALT=\"%28-81%2F16%29-%28-9%29+=+-81%2F16+%2B+144%2F16+=+63%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The height of the arch 1 foot from either base is 63/16 feet, or 3 15/16 feet. </SPAN>\n" );
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