document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=609613>Question 609613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE help me! I need to write an equation in vertex form when I know the vertex and some points.\r<BR>\n" );
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document.write( "1.vertex (0,-1) and (1,1) (-1,1)\r<BR>\n" );
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document.write( "2.vertex (2,4) and (1,1) (3,1) \r<BR>\n" );
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document.write( "3.vertex is (-3,-3) and (2,4) (-8,4)\r<BR>\n" );
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document.write( "Thank you so much!!   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #383837 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=383837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The standard (or general) form of a parabola is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "Given that (2,4) is on the parabola,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a(2)^2\ +\ b(2)\ +\ c\ =\ 4\">\r<BR>\n" );
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document.write( "Given that (1,1) is on the parabola,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a(1)^2\ +\ b(1)\ +\ c\ =\ 1\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "Given that (3,1) is on the parabola,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a(9)^2\ +\ b(3)\ +\ c\ =\ 1\">\r<BR>\n" );
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document.write( "Giving us the 3X3 system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2b\ +\ c\ =\ 4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9a\ +\ 3b\ +\ c\ =\ 1\">\r<BR>\n" );
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document.write( "Verification of the solution set element <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (-3,12-8)\"> is left as an exercise for the student.\r<BR>\n" );
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document.write( "Hence the standard (or general, if you like) form of the equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -3x^2\ +\ 12x\ -\ 8\">\r<BR>\n" );
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document.write( "Complete the square to find vertex form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -3(x^2\ -\ 4x)\ -\ 8\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -3(x^2\ -\ 4x\ +\ 4)\ -\ 8\ +\ 12\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -3(x\ -\ 2)^2\ +\ 4\">\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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