document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042006>Question 1042006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have an algebra 2 question that is about finding an polynomial function that will create three \"hills\" on a graph. These hills can't be crazy numbers and have to be in the first quadrant. The X-axis is the ground. I asked my teacher and she said that I should compress x^6 and it should work out. However, whenever I graph x^6, it always ends up being a parabola. How can I find the correct equation? Thank you so much for the time and effort :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656912 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=656912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^6  is not a parabola by itself.  No compression factor alone will put all of the \"hills\" of x^6 in the first quadrant.  You would want maybe six binomials multiplied, each with an appropriate root which will put x-intercepts to the right of the origin, and then ADD a positive constant of such value that all maxima are ABOVE the x-axis.\r<BR>\n" );
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document.write( "You learn about this topic in College Algebra, or something maybe in highschool more advanced than \"Intermediate\" Algebra.\r<BR>\n" );
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document.write( "Let a, b, c, d, e, be positive real numbers.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-a ALIGN=MIDDLE  ALT=\"x-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- no hills, just a line.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-a%29 ALIGN=MIDDLE  ALT=\"-%28x-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------- again, no hills; just a line.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-a%29%28x-b%29 ALIGN=MIDDLE  ALT=\"-%28x-a%29%28x-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -------- degree two function, would become polynomial; and ONE hill.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-a%29%28x-b%29%28x-c%29 ALIGN=MIDDLE  ALT=\"-%28x-a%29%28x-b%29%28x-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -------degree three function, would become polynomial when multiplied; and ONE hill and ONE valley.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-a%29%28x-b%29%28x-c%29%28x-d%29 ALIGN=MIDDLE  ALT=\"-%28x-a%29%28x-b%29%28x-c%29%28x-d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -------this would become polynomial of degree four.  Two hills and ONE valleys.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-a%29%28x-b%29%28x-c%29%28x-d%29%28x-e%29 ALIGN=MIDDLE  ALT=\"-%28x-a%29%28x-b%29%28x-c%29%28x-d%29%28x-e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -------polynomial degree five.  Two hills and two valleys.\r<BR>\n" );
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document.write( "What comes next? </SPAN>\n" );
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