document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204076>Question 1204076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An arch is in the shape of a parabola. It has a span of 256 meters and a maximum height of 32 meters.\r<BR>\n" );
document.write( "\n" );
document.write( "a. Find the equation of the parabola.<BR>\n" );
document.write( "b. Determine the distance from the center at which the height is 12 meters. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840099 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=840099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. Find the equation of the parabola.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a span of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256 ALIGN=MIDDLE  ALT=\"256\"   DISABLED_style= \"max-width:90%; height:auto;\" >  meters ,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  coordinate of the vertex is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256%2F2=128 ALIGN=MIDDLE  ALT=\"256%2F2=128\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters  and a maximum height of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "Vertex at ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128 ALIGN=MIDDLE  ALT=\"128\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "vertex form of the equation is\r<BR>\n" );
document.write( "\n" );
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;\" > , ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h ALIGN=MIDDLE  ALT=\"+h\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k ALIGN=MIDDLE  ALT=\"+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) is the vertex\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-128%29%5E2%2B32 ALIGN=MIDDLE  ALT=\"y=a%28x-128%29%5E2%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "the parabola starts at ( <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=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) that is a point ( <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=+y ALIGN=MIDDLE  ALT=\"+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%280-128%29%5E2%2B32 ALIGN=MIDDLE  ALT=\"0=a%280-128%29%5E2%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28-128%29%5E2+=+-32 ALIGN=MIDDLE  ALT=\"a%28-128%29%5E2+=+-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16384a=-32 ALIGN=MIDDLE  ALT=\"16384a=-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-32%2F16384 ALIGN=MIDDLE  ALT=\"a=-32%2F16384\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1%2F512 ALIGN=MIDDLE  ALT=\"a=-1%2F512\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "so, equation is\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F512%29%28x-128%29%5E2%2B32 ALIGN=MIDDLE  ALT=\"y=%28-1%2F512%29%28x-128%29%5E2%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b. Determine the distance from the center at which the height is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  meters.\r<BR>\n" );
document.write( "\n" );
document.write( "the height of the arch  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  feet from the center<BR>\n" );
document.write( " center is at  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128 ALIGN=MIDDLE  ALT=\"128\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12 ALIGN=MIDDLE  ALT=\"+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  meters from the center so  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=128%2B12=140 ALIGN=MIDDLE  ALT=\"x=128%2B12=140\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%2F512%29%28140-128%29%5E2%2B32 ALIGN=MIDDLE  ALT=\"y=%28-1%2F512%29%28140-128%29%5E2%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1015%2F32 ALIGN=MIDDLE  ALT=\"y=1015%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=31.7 ALIGN=MIDDLE  ALT=\"y=31.7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  approximately\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-10%2C+260%2C+-10%2C+50%2C+%0D%0Acircle%28128%2C32%2C1.3%29%2C+locate%28128%2C34%2CV%28128%2C32%29%29%2C%0D%0Acircle%28140%2C31.7%2C1.3%29%2C+locate%28140%2C31.7%2Cp%28140%2C31.7%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+260%2C+-10%2C+50%2C+%28-1%2F512%29%28x-128%29%5E2%2B32%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );