document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916237>Question 916237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to graph polynomials. Where do I start? I am lost on these two problems. I don't know what I need to do in order to figure out the graph of:\r<BR>\n" );
document.write( "\n" );
document.write( "f(x) = 4 log(base 4)(x + 8)\r<BR>\n" );
document.write( "\n" );
document.write( "and \r<BR>\n" );
document.write( "\n" );
document.write( "h(x) = (2x+6)(x–3)^2 (x+1)^3\r<BR>\n" );
document.write( "\n" );
document.write( "Is there any way to tell what a graph will look like before starting?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you in advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555981 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=555981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> figure out the graph of: <BR>\n" );
document.write( "f(x) = 4 log(base 4)(x + 8)<BR>\n" );
document.write( "f(x) = 4[log(x+8)/log(4)]<BR>\n" );
document.write( "Sketch the basic curve, y = log(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cln%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cln%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "Shift that graph 8 units to the left because of the (x+8).<BR>\n" );
document.write( "Multiply each y-value by 7/log(4) = 6.64 to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C20%2C%284%2Fln%284%29%29ln%28x%2B8%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C20%2C%284%2Fln%284%29%29ln%28x%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "  <BR>\n" );
document.write( "and <BR>\n" );
document.write( "h(x) = (2x+6)(x–3)^2 (x+1)^3<BR>\n" );
document.write( "f(0) = 6(9)(1) = 54:: So plot (0,54)<BR>\n" );
document.write( "Roots at -3, + 3, and -1:: So plot (-3,0),(-1,0),(3,0)<BR>\n" );
document.write( "Graph does not pass thru (3,0)<BR>\n" );
document.write( "Graph passes thru (-1,0)<BR>\n" );
document.write( "Highest power is x*x^2*x^3 = x^6::<BR>\n" );
document.write( "y goes to +oo as x goes to -oo<BR>\n" );
document.write( "y goes to +oo as x goes to +00<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-50%2C120%2C%282x%2B6%29%28x-3%29%5E2%28x%2B1%29%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-50%2C120%2C%282x%2B6%29%28x-3%29%5E2%28x%2B1%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------- <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );