document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1050020>Question 1050020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for the function f(x), find the maximum number of real zeros,the maximm number of x-intercepts, and the maximum number of turning points that the function can f(x)=x^6-x^3+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665598 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=665598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Know the basic shapes for polynomial functions.\r<BR>\n" );
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document.write( "Degree 6 means maximum six possible x-intercepts;<BR>\n" );
document.write( "Lead coefficient is positive, so left and right sides go upward, and three possible valleys and two possible humps;\r<BR>\n" );
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document.write( "Can you factorize your f(x) ?<BR>\n" );
document.write( "Is it in quadratic form?  Not a question of if it is or is not quadratic, but \"FORM\".<BR>\n" );
document.write( "Is it symmetric around a vertical axis (like, is f(x) an even function)?\r<BR>\n" );
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document.write( "Checking with graphing feature of google search engine, your f seems symmetric around x=0 but seems to have NO real zeros.  Very very very flat between x=5 and x=-5. </SPAN>\n" );
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