document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62769>Question 62769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you help?<BR>\n" );
document.write( "find the vertex and intercepts of the quadratic function f(x)=x^2+x-6.  thank you very much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43604 by </B><A HREF=/tutors/aboutme.mpl?userid=uma><B>uma(370)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=uma><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=43604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The given equation is y = x^2 + x - 6\r<BR>\n" );
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document.write( "This is of the form ax^2 + bx + c = y\r<BR>\n" );
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document.write( "The x co-ordinate of the vertex = -b/2a\r<BR>\n" );
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document.write( "                                = -1/2*1\r<BR>\n" );
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document.write( "                                = -1/2\r<BR>\n" );
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document.write( "Replacing x by -1/2 in the given equation,\r<BR>\n" );
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document.write( "y = (-1/2)^2 + (-1/2) - 6\r<BR>\n" );
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document.write( "  = 1/4  - 1/2  - 6\r<BR>\n" );
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document.write( "  = -1/4  - 6\r<BR>\n" );
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document.write( "  = - 6 1/4\r<BR>\n" );
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document.write( "The vertex = (-1/2, - 25/4)\r<BR>\n" );
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document.write( "To find the y intercept we replace x by 0.\r<BR>\n" );
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document.write( "==> y = 0 + 0 -6\r<BR>\n" );
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document.write( "==> y = - 6\r<BR>\n" );
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document.write( "To find the x intercept we set y = 0\r<BR>\n" );
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document.write( "==> x^2 + x - 6 = 0\r<BR>\n" );
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document.write( "==> x^2 + 3x - 2x - 6 = 0\r<BR>\n" );
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document.write( "==> x(x+3) - 2(x+3) = 0\r<BR>\n" );
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document.write( "==> (x+3)(x-2)= 0\r<BR>\n" );
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document.write( "==> x+ 3 = 0  or  x - 2 = 0\r<BR>\n" );
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document.write( "==> x = - 3  or x = 2\r<BR>\n" );
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document.write( "Thus the x intercepts are -3 and 2 while the y intercept is -6\r<BR>\n" );
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document.write( "Good Luck!!! </SPAN>\n" );
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