document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198214>Question 1198214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arch is in the shape of a parabola. It has a span of 320 meters and a maximum height of 16 meters.<BR>\n" );
document.write( "Find the equation of the parabola (assuming the origin is halfway between the arch's feet). <BR>\n" );
document.write( "Determine the height of the arch 90 meters from the center. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831819 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An arch is in the shape of a parabola.<BR>\n" );
document.write( " It has a span of 320 meters and a maximum height of 16 meters.<BR>\n" );
document.write( "Find the equation of the parabola (assuming the origin is halfway between the arch's feet).<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using the form ax^2 + bx + c<BR>\n" );
document.write( "Using the origin as the midpoint: c = 16 and x = -160 and + 160 when y = 0<BR>\n" );
document.write( "x=-160, y = 0<BR>\n" );
document.write( "-160^2a - 160b + 16= 0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=+160, y = 0<BR>\n" );
document.write( "160^2a + 160b + 16 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "25600a - 160b + 16 = 0<BR>\n" );
document.write( "25600a + 160b + 16 = 0<BR>\n" );
document.write( "--------------------------Adding eliminates b, find a<BR>\n" );
document.write( "51200a + 0 + 32 = 0<BR>\n" );
document.write( "simplify divide by <BR>\n" );
document.write( "1600a + 1 = 0<BR>\n" );
document.write( "1600a = -1<BR>\n" );
document.write( "a = -1/1600<BR>\n" );
document.write( "a = -.000625<BR>\n" );
document.write( "the equation<BR>\n" );
document.write( "-.000625x^2 + 16 = 0<BR>\n" );
document.write( "Looks like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-200%2C+200%2C+-10%2C+20%2C+-.000625x%5E2+%2B+16+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-200%2C+200%2C+-10%2C+20%2C+-.000625x%5E2+%2B+16+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Determine the height of the arch 90 meters from the center.<BR>\n" );
document.write( "x = 90<BR>\n" );
document.write( "y = -.000625(90^2) + 16<BR>\n" );
document.write( "y = -5.0625 + 16<BR>\n" );
document.write( "y = 10.9375 meters (green line<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-200%2C+200%2C+-10%2C+20%2C+-.000625x%5E2+%2B+16%2C+10.9375+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-200%2C+200%2C+-10%2C+20%2C+-.000625x%5E2+%2B+16%2C+10.9375+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );