document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935800>Question 935800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the function f(x)=ax^3+bx^2+cx+d for which f(0)=-2, f(1)=5, f(-1)=3, f(2)=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569157 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Find the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=-2 ALIGN=MIDDLE  ALT=\"f%280%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=5 ALIGN=MIDDLE  ALT=\"f%281%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=3 ALIGN=MIDDLE  ALT=\"f%28-1%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=4 ALIGN=MIDDLE  ALT=\"f%282%29=4\"   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=f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd ALIGN=MIDDLE  ALT=\"f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >....we need to find coefficients\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=-2 ALIGN=MIDDLE  ALT=\"f%280%29=-2\"   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=f%280%29=a%2A0%5E3%2Bb%2A0%5E2%2Bc%2A0-2 ALIGN=MIDDLE  ALT=\"f%280%29=a%2A0%5E3%2Bb%2A0%5E2%2Bc%2A0-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28d=-2%29\"   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=f%281%29=5 ALIGN=MIDDLE  ALT=\"f%281%29=5\"   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=5=a%2A1%5E3%2Bb%2A1%5E2%2Bc%2A1-2 ALIGN=MIDDLE  ALT=\"5=a%2A1%5E3%2Bb%2A1%5E2%2Bc%2A1-2\"   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=5%2B2=a%2Bb%2Bc ALIGN=MIDDLE  ALT=\"5%2B2=a%2Bb%2Bc\"   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=a%2Bb%2Bc=7 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=3 ALIGN=MIDDLE  ALT=\"f%28-1%29=3\"   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=3=a%2A%28-1%29%5E3%2Bb%2A%28-1%29%5E2%2Bc%2A%28-1%29-2 ALIGN=MIDDLE  ALT=\"3=a%2A%28-1%29%5E3%2Bb%2A%28-1%29%5E2%2Bc%2A%28-1%29-2\"   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=3%2B2=-a%2Bb-c ALIGN=MIDDLE  ALT=\"3%2B2=-a%2Bb-c\"   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=-a%2Bb-c=5 ALIGN=MIDDLE  ALT=\"-a%2Bb-c=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=4 ALIGN=MIDDLE  ALT=\"f%282%29=4\"   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=4=a%2A2%5E3%2Bb%2A2%5E2%2Bc%2A2-2 ALIGN=MIDDLE  ALT=\"4=a%2A2%5E3%2Bb%2A2%5E2%2Bc%2A2-2\"   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=4%2B2=8a%2B4b%2B2c ALIGN=MIDDLE  ALT=\"4%2B2=8a%2B4b%2B2c\"   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=6=8a%2B4b%2B2c ALIGN=MIDDLE  ALT=\"6=8a%2B4b%2B2c\"   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=3=4a%2B2b%2Bc ALIGN=MIDDLE  ALT=\"3=4a%2B2b%2Bc\"   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=4a%2B2b%2Bc=3 ALIGN=MIDDLE  ALT=\"4a%2B2b%2Bc=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................eq.3\r<BR>\n" );
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document.write( "use eq.1 and 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=7 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Bb-c=5 ALIGN=MIDDLE  ALT=\"-a%2Bb-c=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................eq.2<BR>\n" );
document.write( "------------------------------------add both\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc-a%2Bb-c=7%2B5 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc-a%2Bb-c=7%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=12 ALIGN=MIDDLE  ALT=\"2b=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=6%29 ALIGN=MIDDLE  ALT=\"highlight%28b=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "go to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b%2Bc=3 ALIGN=MIDDLE  ALT=\"4a%2B2b%2Bc=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................eq.3 substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2%2A6%2Bc=3 ALIGN=MIDDLE  ALT=\"4a%2B2%2A6%2Bc=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B12%2Bc=3 ALIGN=MIDDLE  ALT=\"4a%2B12%2Bc=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3-4a-12 ALIGN=MIDDLE  ALT=\"c=3-4a-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4a-9 ALIGN=MIDDLE  ALT=\"c=-4a-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >....->\r<BR>\n" );
document.write( "\n" );
document.write( "go to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=7 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >..................eq.1 substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B6-4a-9=7 ALIGN=MIDDLE  ALT=\"a%2B6-4a-9=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3a-3=7 ALIGN=MIDDLE  ALT=\"-3a-3=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3a=7%2B3 ALIGN=MIDDLE  ALT=\"-3a=7%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=-10%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28a=-10%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4a-9 ALIGN=MIDDLE  ALT=\"c=-4a-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4%28-10%2F3%29-9 ALIGN=MIDDLE  ALT=\"c=-4%28-10%2F3%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=40%2F3-27%2F3 ALIGN=MIDDLE  ALT=\"c=40%2F3-27%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=13%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28c=13%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the function is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-%2810%2F3%29x%5E3%2B6x%5E2%2B%2813%2F3%29x-2 ALIGN=MIDDLE  ALT=\"f%28x%29=-%2810%2F3%29x%5E3%2B6x%5E2%2B%2813%2F3%29x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );