document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596480>Question 596480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello math tutor. i need help on graphing this. i need to Graph the function: the axis of symmetry, the vertex, and the x-intercepts.\r<BR>\n" );
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document.write( "Problem:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=-2x%5E2%2Bx-4+ ALIGN=MIDDLE  ALT=\"+y=-2x%5E2%2Bx-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thank You! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377757 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=377757\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The axis of symmetry is a vertical line through<BR>\n" );
document.write( "the x-coordinate of the vertex<BR>\n" );
document.write( "The vertex is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the equation <BR>\n" );
document.write( "is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+ax%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=+-b%2F%282a%29+=+-1%2F%282%2A%28-2%29%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-1%2F%282%2A%28-2%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=+-b%2F%282a%29+=+1%2F4+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%28+1%2F4+%29+ ALIGN=MIDDLE  ALT=\"+y%28+1%2F4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%281%2F4%29+=+-2%2A%281%2F4%29%5E2+%2B+1%2F4+-+4+ ALIGN=MIDDLE  ALT=\"+y%281%2F4%29+=+-2%2A%281%2F4%29%5E2+%2B+1%2F4+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%281%2F4%29+=+-1%2F8+%2B+2%2F8+-+32%2F8+ ALIGN=MIDDLE  ALT=\"+y%281%2F4%29+=+-1%2F8+%2B+2%2F8+-+32%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%281%2F4%29+=+-31%2F8+ ALIGN=MIDDLE  ALT=\"+y%281%2F4%29+=+-31%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is at ( 1/4, -31/8 )<BR>\n" );
document.write( "The axis of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+1%2F4+ ALIGN=MIDDLE  ALT=\"+x+=+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Find the x-intercepts by setting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0+ ALIGN=MIDDLE  ALT=\"+y+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2x%5E2+%2B+x+-+4+ ALIGN=MIDDLE  ALT=\"+y+=+-2x%5E2+%2B+x+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2x%5E2+%2B+x+-+4+=+0+ ALIGN=MIDDLE  ALT=\"+-2x%5E2+%2B+x+-+4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-2+ ALIGN=MIDDLE  ALT=\"+a+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+1+ ALIGN=MIDDLE  ALT=\"+b+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-4+ ALIGN=MIDDLE  ALT=\"+c+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A%28-2%29%2A%28-4%29+%29%29+%2F+%282%2A%28-2%29%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A%28-2%29%2A%28-4%29+%29%29+%2F+%282%2A%28-2%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=+x+=+%28-1+%2B-+sqrt%28+1+-+32+%29%29+%2F+%28-4%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt%28+1+-+32+%29%29+%2F+%28-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%281+%2B+sqrt%28+31+%29+%2Ai%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%281+%2B+sqrt%28+31+%29+%2Ai%29+%2F+4+\"   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=+x+=+%281+-+sqrt%28+31+%29+%2Ai%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+x+=+%281+-+sqrt%28+31+%29+%2Ai%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The roots are imaginary, so there are no x-intercepts<BR>\n" );
document.write( "here's a plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-4%2C+4%2C+-10%2C+2%2C+-2x%5E2+%2B+x+-+4+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-4%2C+4%2C+-10%2C+2%2C+-2x%5E2+%2B+x+-+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );