document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154762>Question 154762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the coordinates of the apex of:\r<BR>\n" );
document.write( "\n" );
document.write( "(f*g)(x) if f(x)=x^2+4 and g(x)=x-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113979 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=113979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do you mean the vertex?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%2Ag%29%28x%29 ALIGN=MIDDLE  ALT=\"%28f%2Ag%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2Ag%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29%2Ag%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the function combination\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4%29%2A%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4%29%2A%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=x-3 ALIGN=MIDDLE  ALT=\"g%28x%29=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's FOIL the expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remember, when you FOIL an expression, you follow this procedure:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28x%5E2%29%2B4%29%28highlight%28x%29-3%29 ALIGN=MIDDLE  ALT=\"%28highlight%28x%5E2%29%2B4%29%28highlight%28x%29-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">F</font>irst terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2A%28x%29=x%5E3 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2A%28x%29=x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28x%5E2%29%2B4%29%28x%2Bhighlight%28-3%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28x%5E2%29%2B4%29%28x%2Bhighlight%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">O</font>uter terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2A%28-3%29=-3%2Ax%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2A%28-3%29=-3%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bhighlight%284%29%29%28highlight%28x%29-3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bhighlight%284%29%29%28highlight%28x%29-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">I</font>nner terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2A%28x%29=4%2Ax ALIGN=MIDDLE  ALT=\"%284%29%2A%28x%29=4%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bhighlight%284%29%29%28x%2Bhighlight%28-3%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bhighlight%284%29%29%28x%2Bhighlight%28-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">L</font>ast terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2A%28-3%29=-12 ALIGN=MIDDLE  ALT=\"%284%29%2A%28-3%29=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-3%2Ax%5E2%2B4%2Ax-12 ALIGN=MIDDLE  ALT=\"x%5E3-3%2Ax%5E2%2B4%2Ax-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now collect every term to make a single expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOILs to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-3%2Ax%5E2%2B4%2Ax-12 ALIGN=MIDDLE  ALT=\"x%5E3-3%2Ax%5E2%2B4%2Ax-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%2Ag%29%28x%29=x%5E3-3%2Ax%5E2%2B4%2Ax-12 ALIGN=MIDDLE  ALT=\"%28f%2Ag%29%28x%29=x%5E3-3%2Ax%5E2%2B4%2Ax-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since we're looking at a cubic, this means that the polynomial does not have a vertex. Are you sure that you have the right problem? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );