document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=491587>Question 491587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, my wife is in a college algebra class and we are having a problem with one problem.  The problem is y=x^4-8x^2-9 and we have to list the intercepts and test for symmetry.  We have been able to factor it down to y=(x^2+1)(x-3)(x+3) and then we are stuck here.  The answer in the back of the book shows the intercepts as (3,0) (-3,0) and (0,9) but we are stuck and are unable to come up with any of the answers.  the only intercept we could come up with was (0,-9) but that is wrong.  Thank you for any and all help you can provide.\r<BR>\n" );
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document.write( "Bart </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334694 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=334694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Looking at the graph is often helpful:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-30%2C30%2Cx%5E4-8%2Ax%5E2-9%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-30%2C30%2Cx%5E4-8%2Ax%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This shows the x-intercepts to be:  (-3,0) and (3,0).<BR>\n" );
document.write( "This shows the y-intercept to be:  (0,-9).<BR>\n" );
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document.write( "You also can look this another way using the following substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+x%5E2 ALIGN=MIDDLE  ALT=\"u+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+u%5E2+-8u+-+9 ALIGN=MIDDLE  ALT=\"y+=+u%5E2+-8u+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28u+%2B1%29%28u-9%29 ALIGN=MIDDLE  ALT=\"y+=+%28u+%2B1%29%28u-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%5E2%2B1%29%2A%28x%5E2-9%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%5E2%2B1%29%2A%28x%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%5E2%2B1%29+%2A+%28x-3%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%5E2%2B1%29+%2A+%28x-3%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Clearly, two of the roots are<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
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document.write( "But factoring x^2+1 is a problem because to have to solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In turn, that means:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+-1 ALIGN=MIDDLE  ALT=\"x%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Of course, that defines an imaginary number.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2+=+-1 ALIGN=MIDDLE  ALT=\"i%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Looking back at the original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E4+-8x%5E2+-9 ALIGN=MIDDLE  ALT=\"y+=+x%5E4+-8x%5E2+-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can tell by inspection that when x=0, y = -9.<BR>\n" );
document.write( "That defines the point (0,-9).<BR>\n" );
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document.write( "So, perhaps the book has an error.<BR>\n" );
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document.write( "Done.<BR>\n" );
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