document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24533>Question 24533</A>: <I><SPAN STYLE=\"word-break: break-all;\"> These quadratic equations are kicking my rear, please help. How do I find the Vertex and intecepts of:\r<BR>\n" );
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document.write( "y = -x^2 + 6x -11\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #13056 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=13056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK, well, you do not say if you have done calculus. I  assume you have.\r<BR>\n" );
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document.write( "dy/dx = -2x + 6<BR>\n" );
document.write( "-2x + 6 = 0<BR>\n" );
document.write( "-2x = -6<BR>\n" );
document.write( "x = 3\r<BR>\n" );
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document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%283%29%5E2+%2B+6%283%29+-+11 ALIGN=MIDDLE  ALT=\"y+=+-%283%29%5E2+%2B+6%283%29+-+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> y = -9 + 18 - 11<BR>\n" );
document.write( "--> y = -2\r<BR>\n" );
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document.write( "so, the vertex is at (3,-2)\r<BR>\n" );
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document.write( "As to its intercepts...its solutions..its roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2+%2B+6x+-+11+=+0 ALIGN=MIDDLE  ALT=\"-x%5E2+%2B+6x+-+11+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+6x+%2B+11+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+6x+%2B+11+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looking...it does factorise easily, so use the Quadratic formula. Put the number in to that and you will get a negative square root. Hence no real solution. If you have done Complex Numbers, the find the Complex roots of this equation.\r<BR>\n" );
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document.write( "jon </SPAN>\n" );
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