document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926832>Question 926832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) = -3x(x+2)^2 (x-4)^3\r<BR>\n" );
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document.write( "Perform the Leading Coefficient Test to determine the end behavior of the function. List a^n and n and explain how they lead to your conclusion.\r<BR>\n" );
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document.write( "(Identify all zeros) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562509 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=562509\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:<BR>\n" );
document.write( "f(x) = -3x(x+2)^2 (x-4)^3<BR>\n" );
document.write( "(x+2)^2 will have a leading term of x^2<BR>\n" );
document.write( "(x-4)^3 will have a leading term of x^3<BR>\n" );
document.write( "x * x^2 * x^3 = x^6<BR>\n" );
document.write( "your leading exponent is x^6<BR>\n" );
document.write( "your leading coefficient will be negative because you have 2 leading coefficients that are positive times 1 leading coefficient that is negative to get a negative leading coefficient because a negative times 2 positives is equal to a negative.<BR>\n" );
document.write( "your leading term have an even exponent and your leading coefficient is negative so the equation will fall to the left and fall to the right.<BR>\n" );
document.write( "your zeroes are x = 0, x = -2, x = 4<BR>\n" );
document.write( "the graph of the equation will touch the x-axis at x = -2 and cross the x-axis at x = 0 and x = 4<BR>\n" );
document.write( "this is because the exponent of the (x+2)^2 term is even and the exponent of the (x-4)^3 term and the x term are both odd.<BR>\n" );
document.write( "the graph of your equation looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-3%2C5%2C-1000%2C1000%2C-3x%2A%28x%2B2%29%5E2%2A%28x-4%29%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-3%2C5%2C-1000%2C1000%2C-3x%2A%28x%2B2%29%5E2%2A%28x-4%29%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "here's a reference that can help you understand just what went on.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut35_polyfun.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut35_polyfun.htm</a><BR>\n" );
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