document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102977>Question 102977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The graph of the polynomial function f(x)- Ax^3+Bx^2+Cx+D, <BR>\n" );
document.write( "where and A,B,C,and D are integers, has 3 x-intercepts at 1,2,and -6.<BR>\n" );
document.write( "If the graph passes thought the point M(3,18), <BR>\n" );
document.write( "determine the values of A,B,C and D. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74899 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=74899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An x intercept is a where f(x)=0.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=0 ALIGN=MIDDLE  ALT=\"f%281%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=0 ALIGN=MIDDLE  ALT=\"f%282%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-6%29=0 ALIGN=MIDDLE  ALT=\"f%28-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you know that <BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=18 ALIGN=MIDDLE  ALT=\"f%283%29=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the equations you get <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=0 ALIGN=MIDDLE  ALT=\"f%281%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A1%5E3%2BB%2A1%5E2%2BC%2A1%2BD=0 ALIGN=MIDDLE  ALT=\"A%2A1%5E3%2BB%2A1%5E2%2BC%2A1%2BD=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC%2BD=0 ALIGN=MIDDLE  ALT=\"A%2BB%2BC%2BD=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=0 ALIGN=MIDDLE  ALT=\"f%283%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A2%5E3%2BB%2A2%5E2%2BC%2A2%2BD=0 ALIGN=MIDDLE  ALT=\"A%2A2%5E3%2BB%2A2%5E2%2BC%2A2%2BD=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8A%2B4B%2B2C%2BD=0 ALIGN=MIDDLE  ALT=\"8A%2B4B%2B2C%2BD=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-6%29=0 ALIGN=MIDDLE  ALT=\"f%28-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A%28-6%29%5E3%2BB%2A%28-6%29%5E2%2BC%2A%28-6%29%2BD=0 ALIGN=MIDDLE  ALT=\"A%2A%28-6%29%5E3%2BB%2A%28-6%29%5E2%2BC%2A%28-6%29%2BD=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-216%2AA%2B36%2AB-6%2AC%2BD=0 ALIGN=MIDDLE  ALT=\"-216%2AA%2B36%2AB-6%2AC%2BD=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=18 ALIGN=MIDDLE  ALT=\"f%283%29=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A%283%29%5E3%2BB%2A%283%29%5E2%2BC%2A%283%29%2BD=18 ALIGN=MIDDLE  ALT=\"A%2A%283%29%5E3%2BB%2A%283%29%5E2%2BC%2A%283%29%2BD=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2AA%2B9%2AB%2B3%2AC%2BD=18 ALIGN=MIDDLE  ALT=\"27%2AA%2B9%2AB%2B3%2AC%2BD=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Four equations, four unknowns. <BR>\n" );
document.write( "Since you didn't specify a method to choose, I'll choose a matrix method, if that's OK. <BR>\n" );
document.write( "These equations can be represented as three matrices G, U, and V. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=%28%0D%0A+matrix%28+4%2C+4%2C+%0D%0A+++1%2C1%2C1%2C1%2C%0D%0A8%2C4%2C2%2C1%2C%0D%0A-216%2C36%2C-6%2C1%2C%0D%0A27%2C9%2C3%2C1%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U=%28%0D%0A+matrix%28+4%2C1%2C+%0D%0A++A%2CB%2CC%2CD%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE  ALT=\"U=%28%0D%0A+matrix%28+4%2C1%2C+%0D%0A++A%2CB%2CC%2CD%0D%0A+%29%0D%0A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%28%0D%0A+matrix%28+4%2C1%2C+%0D%0A++0%2C0%2C0%2C18%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE  ALT=\"V=%28%0D%0A+matrix%28+4%2C1%2C+%0D%0A++0%2C0%2C0%2C18%0D%0A+%29%0D%0A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where [G]x[U]=[V]<BR>\n" );
document.write( "Then [U]=[G]inv x [V]<BR>\n" );
document.write( "Find the inverse of [G](using EXCEL) and multiply by [V]<BR>\n" );
document.write( "The inverse of G is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+G%5Binv%5D=%28matrix%28+4%2C+4%2C+%0D%0A+++++1%2F14%2C+-1%2F8%2C+-1%2F504%2C++1%2F18%2C%0D%0A+++++1%2F14%2C+-2%2F8%2C++6%2F504%2C++3%2F18%2C%0D%0A+++-24%2F14%2C+21%2F8%2C-11%2F504%2C-16%2F18%2C%0D%0A++++36%2F14%2C-18%2F8%2C++6%2F504%2C+12%2F18%0D%0A+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since [V] has all values of zero except the last value. The solution matrix,[U], is 18 multplied by the last column of the inverse matrix or <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1 ALIGN=MIDDLE  ALT=\"A=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=3 ALIGN=MIDDLE  ALT=\"B=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-16 ALIGN=MIDDLE  ALT=\"C=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=12 ALIGN=MIDDLE  ALT=\"D=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );