document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204304>Question 1204304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation and sketch an example of a quartic function with the zeros at  -  4,  -  1, 2 (order 2). Be sure to include an image of your solution.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840469 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The polynomial equation is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=a%28x%2B4%29%28x%2B1%29%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"p%28x%29=a%28x%2B4%29%28x%2B1%29%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The degree of the polynomial is 4, so the end behavior is the same both to the left and to the right.  If the leading coefficient a is positive, the end behavior in both directions is upward; if it is negative, the end behavior in both directions is downward.<br><BR>\n" );
document.write( "Assume that the leading coefficient is positive.  Then we have...<br><BR>\n" );
document.write( "end behavior upward to the left;<BR>\n" );
document.write( "a single root at x=-4, so the graph crosses the x-axis, making the function value negative;<BR>\n" );
document.write( "a single root at x=-1, so the graph crosses the x-axis, making the function value positive;<BR>\n" );
document.write( "a double root at x=2, so the graph just touches the x-axis, after which the function value remains positive; and<BR>\n" );
document.write( "end behavior upward to the right.<br><BR>\n" );
document.write( "A graph showing that behavior, using a leading coefficient of a=1:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-100%2C100%2C%28x%2B4%29%28x%2B1%29%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-100%2C100%2C%28x%2B4%29%28x%2B1%29%28x-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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