document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206114>Question 1206114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial of the form<BR>\n" );
document.write( "f(x)= ax^3+bx^2+cx+d<BR>\n" );
document.write( "such that f(0)=-5, f(-1)=-6, f(3)=4, and f(4)=-4. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843347 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=843347\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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;\" >\r<BR>\n" );
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document.write( "if<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=-5 ALIGN=MIDDLE  ALT=\"f%280%29=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-5 ALIGN=MIDDLE  ALT=\"f%28x%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%2A0%5E3%2Bb%2A0%5E2%2Bc%2A0%2Bd ALIGN=MIDDLE  ALT=\"-5=+a%2A0%5E3%2Bb%2A0%5E2%2Bc%2A0%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=-5 ALIGN=MIDDLE  ALT=\"d=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1\r<BR>\n" );
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document.write( "so far we have <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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=-6 ALIGN=MIDDLE  ALT=\"f%28-1%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-6 ALIGN=MIDDLE  ALT=\"f%28x%29=-6\"   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=+a%2A%28-1%29%5E3%2Bb%2A%28-1%29%5E2%2Bc%2A%28-1%29-5 ALIGN=MIDDLE  ALT=\"-6=+a%2A%28-1%29%5E3%2Bb%2A%28-1%29%5E2%2Bc%2A%28-1%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=-6%2B5=+-a%2Bb-c ALIGN=MIDDLE  ALT=\"-6%2B5=+-a%2Bb-c\"   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=a=b-c%2B1 ALIGN=MIDDLE  ALT=\"a=b-c%2B1\"   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%283%29=4 ALIGN=MIDDLE  ALT=\"f%283%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=4 ALIGN=MIDDLE  ALT=\"f%28x%29=4\"   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=4=+a%2A%283%29%5E3%2Bb%2A%283%29%5E2%2Bc%2A%283%29-5 ALIGN=MIDDLE  ALT=\"4=+a%2A%283%29%5E3%2Bb%2A%283%29%5E2%2Bc%2A%283%29-5\"   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=4%2B5=27a%2B9b%2B3c ALIGN=MIDDLE  ALT=\"4%2B5=27a%2B9b%2B3c\"   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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27a=9-9b-3c ALIGN=MIDDLE  ALT=\"27a=9-9b-3c\"   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=9%2F27-9b%2F27-3c%2F27 ALIGN=MIDDLE  ALT=\"a=9%2F27-9b%2F27-3c%2F27\"   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=1%2F3-b%2F3-c%2F9 ALIGN=MIDDLE  ALT=\"a=1%2F3-b%2F3-c%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.3\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29=-4 ALIGN=MIDDLE  ALT=\"f%284%29=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-4 ALIGN=MIDDLE  ALT=\"f%28x%29=-4\"   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=-4=+a%2A%284%29%5E3%2Bb%2A%284%29%5E2%2Bc%2A%284%29-5 ALIGN=MIDDLE  ALT=\"-4=+a%2A%284%29%5E3%2Bb%2A%284%29%5E2%2Bc%2A%284%29-5\"   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=-4%2B5=64a++%2B+16b+%2B+4c+ ALIGN=MIDDLE  ALT=\"-4%2B5=64a++%2B+16b+%2B+4c+\"   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+=+1%2F64+%28-16b+-+4c+%2B+1%29 ALIGN=MIDDLE  ALT=\"a+=+1%2F64+%28-16b+-+4c+%2B+1%29\"   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=-b%2F4+-+c%2F16+%2B+1%2F64 ALIGN=MIDDLE  ALT=\"a=-b%2F4+-+c%2F16+%2B+1%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.4\r<BR>\n" );
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document.write( "from eq.2 and eq.3 we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-c%2B1=1%2F3-b%2F3-c%2F9 ALIGN=MIDDLE  ALT=\"b-c%2B1=1%2F3-b%2F3-c%2F9\"   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+=+%283+b%29%2F2+%2B+3%2F4 ALIGN=MIDDLE  ALT=\"c+=+%283+b%29%2F2+%2B+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.5\r<BR>\n" );
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document.write( "from eq.2 and eq.4 we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-c%2B1=-b%2F4+-+c%2F16+%2B+1%2F64 ALIGN=MIDDLE  ALT=\"b-c%2B1=-b%2F4+-+c%2F16+%2B+1%2F64\"   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+=+%284+b%29%2F3+%2B+21%2F20 ALIGN=MIDDLE  ALT=\"c+=+%284+b%29%2F3+%2B+21%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.6\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "from eq.5 and 6 we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+b%29%2F2+%2B+3%2F4=%284+b%29%2F3+%2B+21%2F20 ALIGN=MIDDLE  ALT=\"%283+b%29%2F2+%2B+3%2F4=%284+b%29%2F3+%2B+21%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <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=b+=+9%2F5 ALIGN=MIDDLE  ALT=\"b+=+9%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\n" );
document.write( "go to eq.5, 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=c+=+%283+%289%2F5%29%29%2F2+%2B+3%2F4 ALIGN=MIDDLE  ALT=\"c+=+%283+%289%2F5%29%29%2F2+%2B+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.5\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=69%2F20 ALIGN=MIDDLE  ALT=\"c=69%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "go to eq.2, 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=9%2F5-69%2F20%2B1 ALIGN=MIDDLE  ALT=\"a=9%2F5-69%2F20%2B1\"   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=a=-13%2F20 ALIGN=MIDDLE  ALT=\"a=-13%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your function is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%28-13%2F20%29x%5E3%2B%289%2F5%29x%5E2%2B%2869%2F20%29x-5 ALIGN=MIDDLE  ALT=\"f%28x%29=+%28-13%2F20%29x%5E3%2B%289%2F5%29x%5E2%2B%2869%2F20%29x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );