document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113794>Question 113794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph f(x)=x^4-4x^2\r<BR>\n" );
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document.write( "First find the x-intercepts then evaluate f(-3),f(-1),f(1),f(3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82810 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=82810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4-4x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%28x%5E2-4%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%28x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%28x-2%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%28x-2%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4 ALIGN=MIDDLE  ALT=\"x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the difference of squares to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now to find the x-intercepts, set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to zero and solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%28x-2%29%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"x%5E2%28x-2%29%28x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Break up the equation using the zero product property\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=0 ALIGN=MIDDLE  ALT=\"x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=0 ALIGN=MIDDLE  ALT=\"x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=0 ALIGN=MIDDLE  ALT=\"x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x in each case\r<BR>\n" );
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document.write( "So our solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means the x-intercepts are (0,0), (2,0), and (-2,0)\r<BR>\n" );
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document.write( "Notice if we graph, we get\r<BR>\n" );
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document.write( "and we can see that the x-intercepts are (0,0), (2,0), and (-2,0)\r<BR>\n" );
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document.write( "------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Let's evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29 ALIGN=MIDDLE  ALT=\"f%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4-4x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=%28-3%29%5E4-4%28-3%29%5E2 ALIGN=MIDDLE  ALT=\"f%28-3%29=%28-3%29%5E4-4%28-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with -3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=%2881%29-4%28-3%29%5E2 ALIGN=MIDDLE  ALT=\"f%28-3%29=%2881%29-4%28-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E4 ALIGN=MIDDLE  ALT=\"%28-3%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 81.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=%2881%29-4%289%29 ALIGN=MIDDLE  ALT=\"f%28-3%29=%2881%29-4%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 9.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=%2881%29-36 ALIGN=MIDDLE  ALT=\"f%28-3%29=%2881%29-36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4 and 9 to get  -36\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=45 ALIGN=MIDDLE  ALT=\"f%28-3%29=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "-----------Now let's evaluate another value---------\r<BR>\n" );
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document.write( "Let's evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29 ALIGN=MIDDLE  ALT=\"f%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4-4x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=%28-1%29%5E4-4%28-1%29%5E2 ALIGN=MIDDLE  ALT=\"f%28-1%29=%28-1%29%5E4-4%28-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with -1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=%281%29-4%28-1%29%5E2 ALIGN=MIDDLE  ALT=\"f%28-1%29=%281%29-4%28-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E4 ALIGN=MIDDLE  ALT=\"%28-1%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=%281%29-4%281%29 ALIGN=MIDDLE  ALT=\"f%28-1%29=%281%29-4%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E2 ALIGN=MIDDLE  ALT=\"%28-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=%281%29-4 ALIGN=MIDDLE  ALT=\"f%28-1%29=%281%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4 and 1 to get  -4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=-3 ALIGN=MIDDLE  ALT=\"f%28-1%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "-----------Now let's evaluate another value---------\r<BR>\n" );
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document.write( "Let's evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29 ALIGN=MIDDLE  ALT=\"f%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4-4x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=%281%29%5E4-4%281%29%5E2 ALIGN=MIDDLE  ALT=\"f%281%29=%281%29%5E4-4%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=%281%29-4%281%29%5E2 ALIGN=MIDDLE  ALT=\"f%281%29=%281%29-4%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%5E4 ALIGN=MIDDLE  ALT=\"%281%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=%281%29-4%281%29 ALIGN=MIDDLE  ALT=\"f%281%29=%281%29-4%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%5E2 ALIGN=MIDDLE  ALT=\"%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=%281%29-4 ALIGN=MIDDLE  ALT=\"f%281%29=%281%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4 and 1 to get  -4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=-3 ALIGN=MIDDLE  ALT=\"f%281%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "-----------Now let's evaluate another value---------\r<BR>\n" );
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document.write( "Let's evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29 ALIGN=MIDDLE  ALT=\"f%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E4-4x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E4-4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=%283%29%5E4-4%283%29%5E2 ALIGN=MIDDLE  ALT=\"f%283%29=%283%29%5E4-4%283%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace each x with 3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=%2881%29-4%283%29%5E2 ALIGN=MIDDLE  ALT=\"f%283%29=%2881%29-4%283%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%5E4 ALIGN=MIDDLE  ALT=\"%283%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 81.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=%2881%29-4%289%29 ALIGN=MIDDLE  ALT=\"f%283%29=%2881%29-4%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%5E2 ALIGN=MIDDLE  ALT=\"%283%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 9.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=%2881%29-36 ALIGN=MIDDLE  ALT=\"f%283%29=%2881%29-36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply -4 and 9 to get  -36\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=45 ALIGN=MIDDLE  ALT=\"f%283%29=45\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms<BR>\n" );
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