document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1063017>Question 1063017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial function whose graph passes through each set of points. (-2,10) (-1,-4) (0,-2) (1,-2)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #678042 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=678042\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Four points could go well for degree-three polynomial function.<BR>\n" );
document.write( "Unknown constant coefficients, a, b, c, d;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E3%2Bbx%5E2%2Bcx%2Bd=y ALIGN=MIDDLE  ALT=\"ax%5E3%2Bbx%5E2%2Bcx%2Bd=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the given points to form four specific degree-three equations for a system.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%28-2%29%5E3%2Aa%2B%28-2%29%5E2%2Ab%2B%28-2%29c%2Bd=10%2C%28-1%29%5E3%2Aa%2B%28-1%29%5E2%2Ab%2B%28-1%29c%2Bd=-4%2C0%5E3%2Aa%2B0%5E2%2Ab%2B0%2Ac%2Bd=-2%2C1%5E3%2Aa%2B1%5E2%2Ab%2B1%2Ac%2Bd=-2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-8a%2B4b-2c%2Bd=10%2C-a%2Bb-c%2Bd=-4%2Cd=-2%2Ca%2Bb%2Bc%2Bd=-2%29 ALIGN=MIDDLE  ALT=\"system%28-8a%2B4b-2c%2Bd=10%2C-a%2Bb-c%2Bd=-4%2Cd=-2%2Ca%2Bb%2Bc%2Bd=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the system to solve.\r<BR>\n" );
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document.write( "Substituting for d makes for a simpler three-variable system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-8a%2B4b-2c=12%2C-a%2Bb-c=-2%2Ca%2Bb%2Bc=0%29 ALIGN=MIDDLE  ALT=\"system%28-8a%2B4b-2c=12%2C-a%2Bb-c=-2%2Ca%2Bb%2Bc=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(-1/2)*E1 gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%284a-2b%2Bc=-6%2Ca-b%2Bc=2%2Ca%2Bb%2Bc=0%29 ALIGN=MIDDLE  ALT=\"system%284a-2b%2Bc=-6%2Ca-b%2Bc=2%2Ca%2Bb%2Bc=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "E1-E3 and E2-E3 give<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a-b=-2%2Cb=-1%29 ALIGN=MIDDLE  ALT=\"system%28a-b=-2%2Cb=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This very simple system gives two of the variables.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28b=-1%2Ca=-3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28b=-1%2Ca=-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d was already found early, and with a, b, d, all now found, c can be evaluated, whichever equation you want.\r<BR>\n" );
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