document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930999>Question 930999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y-axis at 2.If f(1)=1, and f(-2) =-2, find f(-1) and write the complete function.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #565402 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=565402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cubic polynomial function:\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;\" >\r<BR>\n" );
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document.write( "given:<BR>\n" );
document.write( "has leading coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2+ ALIGN=MIDDLE  ALT=\"+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28a=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so far we know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=-2x%5E3%2Bbx%5E2%2Bcx%2Bd ALIGN=MIDDLE  ALT=\"+f%28x%29+=-2x%5E3%2Bbx%5E2%2Bcx%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and intercepts the y-axis at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"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;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=-2x%5E3%2Bbx%5E2%2Bcx%2B2 ALIGN=MIDDLE  ALT=\"+f%28x%29+=-2x%5E3%2Bbx%5E2%2Bcx%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=1 ALIGN=MIDDLE  ALT=\"f%281%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%281%29+=-2%281%29%5E3%2Bb%281%29%5E2%2Bc%281%29%2B2=1 ALIGN=MIDDLE  ALT=\"+f%281%29+=-2%281%29%5E3%2Bb%281%29%5E2%2Bc%281%29%2B2=1\"   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=+-2%2Bb%2Bc%2B2=1 ALIGN=MIDDLE  ALT=\"+-2%2Bb%2Bc%2B2=1\"   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=+b%2Bc=1 ALIGN=MIDDLE  ALT=\"+b%2Bc=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1\r<BR>\n" );
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document.write( " and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29+=-2 ALIGN=MIDDLE  ALT=\"f%28-2%29+=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  =>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28-2%29+=-2%28-2%29%5E3%2Bb%28-2%29%5E2%2Bc%28-2%29%2B2=-2 ALIGN=MIDDLE  ALT=\"+f%28-2%29+=-2%28-2%29%5E3%2Bb%28-2%29%5E2%2Bc%28-2%29%2B2=-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=+-2%28-8%29%2Bb%284%29%2Bc%28-2%29%2B2=-2 ALIGN=MIDDLE  ALT=\"+-2%28-8%29%2Bb%284%29%2Bc%28-2%29%2B2=-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=16%2B4b-2c%2B2=-2 ALIGN=MIDDLE  ALT=\"16%2B4b-2c%2B2=-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=+4b-2c=-20 ALIGN=MIDDLE  ALT=\"+4b-2c=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2\r<BR>\n" );
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document.write( "solve the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%2Bc=1 ALIGN=MIDDLE  ALT=\"+b%2Bc=1\"   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=+4b-2c=-20 ALIGN=MIDDLE  ALT=\"+4b-2c=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2<BR>\n" );
document.write( "_________________________\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%2Bc=1 ALIGN=MIDDLE  ALT=\"+b%2Bc=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1 ...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=1-c ALIGN=MIDDLE  ALT=\"+b=1-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >...substitute in eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%281-c%29-2c=-20 ALIGN=MIDDLE  ALT=\"+4%281-c%29-2c=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2...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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4-4c-2c=-20 ALIGN=MIDDLE  ALT=\"+4-4c-2c=-20\"   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=+4-6c=-20 ALIGN=MIDDLE  ALT=\"+4-6c=-20\"   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%2B20=6c ALIGN=MIDDLE  ALT=\"+4%2B20=6c\"   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=+24=6c ALIGN=MIDDLE  ALT=\"+24=6c\"   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=+24%2F6=c ALIGN=MIDDLE  ALT=\"+24%2F6=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=highlight%28c=4%29 ALIGN=MIDDLE  ALT=\"highlight%28c=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find <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=1-c ALIGN=MIDDLE  ALT=\"+b=1-c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=1-4 ALIGN=MIDDLE  ALT=\"+b=1-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28+b=-3%29 ALIGN=MIDDLE  ALT=\"highlight%28+b=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " the complete 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+=-2x%5E3-3x%5E2%2B4x%2B2 ALIGN=MIDDLE  ALT=\"+f%28x%29+=-2x%5E3-3x%5E2%2B4x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\n" );
document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29 ALIGN=MIDDLE  ALT=\"f%28-1%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%28-1%29+=-2%28-1%29%5E3-3%28-1%29%5E2%2B4%28-1%29%2B2 ALIGN=MIDDLE  ALT=\"+f%28-1%29+=-2%28-1%29%5E3-3%28-1%29%5E2%2B4%28-1%29%2B2\"   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=+f%28-1%29+=-2%28-1%29-3%281%29%2B4%28-1%29%2B2 ALIGN=MIDDLE  ALT=\"+f%28-1%29+=-2%28-1%29-3%281%29%2B4%28-1%29%2B2\"   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=+f%28-1%29+=2-3-4%2B2 ALIGN=MIDDLE  ALT=\"+f%28-1%29+=2-3-4%2B2\"   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=+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( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28-2%29+=-2%28-2%29%5E3-3%28-2%29%5E2%2B4%28-2%29%2B2 ALIGN=MIDDLE  ALT=\"+f%28-2%29+=-2%28-2%29%5E3-3%28-2%29%5E2%2B4%28-2%29%2B2\"   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=+f%28-2%29+=-2%28-8%29-3%284%29%2B4%28-2%29%2B2 ALIGN=MIDDLE  ALT=\"+f%28-2%29+=-2%28-8%29-3%284%29%2B4%28-2%29%2B2\"   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=+f%28-2%29+=16-12-8%2B2 ALIGN=MIDDLE  ALT=\"+f%28-2%29+=16-12-8%2B2\"   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=+f%28-2%29+=4-8%2B2 ALIGN=MIDDLE  ALT=\"+f%28-2%29+=4-8%2B2\"   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=+f%28-2%29+=6-8 ALIGN=MIDDLE  ALT=\"+f%28-2%29+=6-8\"   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=+f%28-2%29+=-2 ALIGN=MIDDLE  ALT=\"+f%28-2%29+=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...as given\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2Ccircle%281%2C1%2C.15%29%2Clocate%281%2C1%2Cp%281%2C1%29%29%2Ccircle%280%2C2%2C.15%29%2Clocate%280%2C2%2Cp%280%2C2%29%29%2Ccircle%28-2%2C-2%2C.15%29%2Clocate%28-2%2C-2%2Cp%28-2%2C-2%29%29%2C+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+-2x%5E3-3x%5E2%2B4x%2B2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );