document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=752747>Question 752747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I'm having trouble figuring out a parabola's equation. The Y intercept is (0,6), the vertex is (2,8). These are the only points given. Can you please explain to me how to work out the equation/what it is?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks a lot,<BR>\n" );
document.write( "Nathan  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458002 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=458002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+ ALIGN=MIDDLE  ALT=\"+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the y-intercept, <BR>\n" );
document.write( "(0,6),so now you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+6+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x-coordinate of the vertex, <BR>\n" );
document.write( "(2,8), is <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;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+2+=+-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=+4a+=+-b+ ALIGN=MIDDLE  ALT=\"+4a+=+-b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4a+ ALIGN=MIDDLE  ALT=\"+b+=+-4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So far, you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+-+4a%2Ax+%2B+6+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+-+4a%2Ax+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now plug in the point ( 2,8 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+=+a%2A2%5E2+-+4a%2A2+%2B+6+ ALIGN=MIDDLE  ALT=\"+8+=+a%2A2%5E2+-+4a%2A2+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+=+4a+-+8a+%2B+6+ ALIGN=MIDDLE  ALT=\"+8+=+4a+-+8a+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+=+-4a+%2B+6+ ALIGN=MIDDLE  ALT=\"+8+=+-4a+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+=+-2+ ALIGN=MIDDLE  ALT=\"+4a+=+-2+\"   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%2F2+ ALIGN=MIDDLE  ALT=\"+a+=+-1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4a+ ALIGN=MIDDLE  ALT=\"+b+=+-4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=+2+ ALIGN=MIDDLE  ALT=\"+b=+2+\"   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=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%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=+y+=+%28-1%2F2%29%2Ax%5E2+%2B+2x+%2B+6+ ALIGN=MIDDLE  ALT=\"+y+=+%28-1%2F2%29%2Ax%5E2+%2B+2x+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Is the vertex at (2,8) ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+2+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+2+=+-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=+2+=+-2%2F%282%2A%28-1%2F2%29%29+ ALIGN=MIDDLE  ALT=\"+2+=+-2%2F%282%2A%28-1%2F2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+2+ ALIGN=MIDDLE  ALT=\"+2+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+=+%28-1%2F2%29%2A2%5E2+%2B+2%2A2+%2B+6+ ALIGN=MIDDLE  ALT=\"+8+=+%28-1%2F2%29%2A2%5E2+%2B+2%2A2+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+=+%28-1%2F2%29%2A4+%2B+4+%2B+6+ ALIGN=MIDDLE  ALT=\"+8+=+%28-1%2F2%29%2A4+%2B+4+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+=+-2+%2B+10+ ALIGN=MIDDLE  ALT=\"+8+=+-2+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+=+8+ ALIGN=MIDDLE  ALT=\"+8+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Here's a plot of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C++%28-1%2F2%29%2Ax%5E2+%2B+2x+%2B+6+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C++%28-1%2F2%29%2Ax%5E2+%2B+2x+%2B+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );