document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936364>Question 936364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a cubic function that passes through the following points: (-2,0) (3,0) (-1,0) and (1,2). Explain how you got the answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569803 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general standard cubic:<BR>\n" );
document.write( "ax^3 + bx^2 + cx + d = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "from the first 3 points (-2,0) (3,0) (-1,0), we have 3 roots at:<BR>\n" );
document.write( "(x + 2)(x - 3)(x + 1)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "so the equation is as follows, where k is an unknown constant:<BR>\n" );
document.write( "(x + 2)(x - 3)(x + 1) + k = 0<BR>\n" );
document.write( "(xx - x - 6)(x + 1) + k = 0<BR>\n" );
document.write( "xxx + xx - xx - x - 6x - 6 + k = 0<BR>\n" );
document.write( "xxx - 7x - 6 + k = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "but from the 4th point (1,2) we know that:<BR>\n" );
document.write( "xxx - 7x - 6 + k = 0<BR>\n" );
document.write( "1*1*1 - 7*1 - 6 + k = 0<BR>\n" );
document.write( "-12 + k = 0<BR>\n" );
document.write( "k = 12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "combining the constants, the equation is:<BR>\n" );
document.write( "xxx - 7x - 6 + k = 0<BR>\n" );
document.write( "xxx - 7x - 6 + 12 = 0<BR>\n" );
document.write( "xxx - 7x + 6 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "x^3 - 7x + 6 = 0<BR>\n" );
document.write( "---<BR>\n" );
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document.write( "---<BR>\n" );
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document.write( "---<BR>\n" );
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document.write( "---<BR>\n" );
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document.write( "--- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );