document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=649759>Question 649759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you could please help me solve this whole entire input output equation that would be great! Ok    here is the input/ top row - 1 2 4 5 8 12 _ <BR>\n" );
document.write( "                 here is the output/ bottom row   -3 9 21 _ _ _ 57\r<BR>\n" );
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document.write( "what is the rule and the numbers for the top and bottom, if you could message me by 7:00am tomorrow 9/12/12 morning that would be great. Thank you1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407092 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=407092\">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( "You have three fully described non-collinear points.  I'm going to presume that you were just being sloppy with the hyphen where you started the first row because if the first input value is -1, then the answer comes out with sloppy decimal fractions.\r<BR>\n" );
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document.write( "Since you have three non-collinear points, you can uniquely describe either a circle or a parabola, but since this looks like you want a function, I'm going to go with a parabola.\r<BR>\n" );
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document.write( "A general function that graphs to a parabola is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \rho(x)\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
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document.write( "Substituting the values for the first three points:\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\ =\ -3\">\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\ =\ 9\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a(4)^2\ +\ b(4)\ +\ c\ =\ 21\">\r<BR>\n" );
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document.write( "Which leads to the following 3X3 linear system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ =\ -3\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4a\ +\ 2b\ +\ c\ =\ 9\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 16a\ +\ 4b\ +\ c\ =\ 21\">\r<BR>\n" );
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document.write( "You have some work to do:\r<BR>\n" );
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document.write( "Step 1:  Solve the 3X3 linear system to get your function coefficients.\r<BR>\n" );
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document.write( "Step 2:  Evaluate your function at 5, 8, and 12.\r<BR>\n" );
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document.write( "Step 3:  Set your function equal to 57 and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">\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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