document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=325939>Question 325939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me find this equation: Find the equation of the vertical parabola passing through (0,-6);(1,-3);(2,6). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #233311 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=233311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The equation of a general parabola with a vertical axis of symmetry is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ y\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "Substituting the coordinates of the first given point:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ -6\ =\ a(0)^2\ +\ b(0)\ +\ c\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ -6\ =\ c\">\r<BR>\n" );
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document.write( "Substituting the coordinates of the second given point:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ -3\ =\ a(1)^2\ +\ b(1)\ +\ c\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ -3\ =\ a\ +\ b\ +\ c\">\r<BR>\n" );
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document.write( "Substituting the coordinates of the third point:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ 6\ =\ a(4)^2\ +\ b(2)\ +\ c\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ 6\ =\ 4a\ +\ 2b\ +\ c\">\r<BR>\n" );
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document.write( "Substituting the value we have determined for c:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ -3\ =\ a\ +\ b\ -\ 6\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ a\ +\ b\ =\ 3\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ 6\ =\ 4a\ +\ 2b\ -\ 6\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2b\ =\ 12\">\r<BR>\n" );
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document.write( "Now just solve the 2 X 2 system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ \ \,a\ +\ \ b\ =\ 3\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2b\ =\ 12\">\r<BR>\n" );
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document.write( "and you will have all three coefficients to fill in the general equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \ \ \ \ \ \ \ \ \ y\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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