document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=707573>Question 707573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for a cubic polynomial p(x) with leading coefficient -1 whose graph passes through the point (2, 8) and is tangent to the x-axis at the origin.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #435754 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=435754\">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=p%28x%29=-x%5E3%2Bbx%5E2%2Bcx%2Bd ALIGN=MIDDLE  ALT=\"p%28x%29=-x%5E3%2Bbx%5E2%2Bcx%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "derivative of p(0) must be zero because of tangent at the origin.  Taking derivative, setting it equal zero, seems c=0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(2)=8, so carrying this through did not seem to help.  8=-8+4b+d, not too useful.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Point (0,0) must satisfy our p(x) polynomial, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-0%5E3%2Bb%2A0%5E2%2Bd ALIGN=MIDDLE  ALT=\"0=-0%5E3%2Bb%2A0%5E2%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "apparantly d=0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So far we seem to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=-x%5E3%2Bbx%5E2 ALIGN=MIDDLE  ALT=\"p%28x%29=-x%5E3%2Bbx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Let's try point (2,8) again.  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=-%28x%5E2%29%28x-b%29 ALIGN=MIDDLE  ALT=\"p%28x%29=-%28x%5E2%29%28x-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, also.<BR>\n" );
document.write( "Using the point, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=-%282%29%5E2%2A%282-b%29 ALIGN=MIDDLE  ALT=\"8=-%282%29%5E2%2A%282-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "b=4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "THIS should work well:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=-%28x%5E2%29%28x-4%29 ALIGN=MIDDLE  ALT=\"p%28x%29=-%28x%5E2%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );