document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=623652>Question 623652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What polynomial has a graph that passes through the given points (-2, 2) (-1, -1) (1, 5) (3, 67)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #392304 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=392304\">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( "Since you have 4 points, you need a 4-term, which is to say a 3rd degree, polynomial of the form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \phi(x)\ =\ ax^3\ +\ bx^2\ +\ cx\ +\ d\">\r<BR>\n" );
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document.write( "Using the data in your first point:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \phi(-2)\ =\ a(-2)^3\ +\ b(-2)^2\ +\ c(-2)\ +\ d\ =\ 2\">\r<BR>\n" );
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document.write( "which yields a four variable linear equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -8a\ +\ 4b\ -\ 2c\ +\ 1\ =\ 2\">\r<BR>\n" );
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document.write( "Using similar logic, write three more 4 variable linear equations using the data in the other three points yielding, in toto, a 4X4 system of equations.\r<BR>\n" );
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document.write( "Solve the 4X4 system by any convenient (relatively speaking that is) means.  I used the MDETERM function in Excel and then apply Cramer's Rule.  The ordered quadruple element of the solution set to the 4X4 (it is an independent and consistent system, by the way) consists of the 4 coefficients of your desired polynomial.\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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