document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154932>Question 1154932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the formulas below could be a polynomial with all of the following properties: its only zeros are x=−9,−3,3, it has its y-intercept at y=4, and its long-run behavior is y→−∞ as x→±∞? Select every formula that has all of these properties.<BR>\n" );
document.write( "A. y=−4/729(x−9)(x−3)(x+3)\r<BR>\n" );
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document.write( "B. y=−4/81(x+9)(x+3)(x−3)\r<BR>\n" );
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document.write( "C. y=−4/59049(x+9)4(x+3)(x−3)\r<BR>\n" );
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document.write( "D. y=−4/243(x+9)(x+3)(x−3)2\r<BR>\n" );
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document.write( "E. y=−4/729(x+9)2(x+3)(x−3)\r<BR>\n" );
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document.write( "F. y=−4/243(x+9)(x+3)2(x−3)\r<BR>\n" );
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document.write( "G. y=4/243(x+9)(x+3)(x−3)2<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 #777464 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=777464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4%2F729%29%28x-9%29%28x-3%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y=%28-4%2F729%29%28x-9%29%28x-3%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4%2F81%29%28x%2B9%29%28x%2B3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y=%28-4%2F81%29%28x%2B9%29%28x%2B3%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4%2F59049%29%28x%2B9%29%5E4%28x%2B3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y=%28-4%2F59049%29%28x%2B9%29%5E4%28x%2B3%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "D. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4%2F243%29%28x%2B9%29%28x%2B3%29%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28-4%2F243%29%28x%2B9%29%28x%2B3%29%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "E. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4%2F729%29%28x%2B9%29%5E2%28x%2B3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y=%28-4%2F729%29%28x%2B9%29%5E2%28x%2B3%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "F. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-4%2F243%29%28x%2B9%29%28x%2B3%29%5E2%28x-3%29 ALIGN=MIDDLE  ALT=\"y=%28-4%2F243%29%28x%2B9%29%28x%2B3%29%5E2%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "G. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F243%29%28x%2B9%29%28x%2B3%29%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"y=%284%2F243%29%28x%2B9%29%28x%2B3%29%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The specified long-term behavior means the polynomial has to be even degree with a negative leading coefficient.  Choices C, D, E, and F satisfy that requirement.<br><BR>\n" );
document.write( "With zeros at -9, -3, and 3, the binomial factors have to be (x+9), (x+3), and (x-3).  Choices C, D, E, and F satisfy that requirement also.<br><BR>\n" );
document.write( "Any of those choices that have a y-intercept of 4 will satisfy all the requirements.<br><BR>\n" );
document.write( "Without doing the multiplication, it can be seen that the y-intercept for choice D is negative, while the y-intercepts for choices C, E, and F will be positive.<br><BR>\n" );
document.write( "Any of those three will satisfy all the requirements if the y-intercept is 4.<br><BR>\n" );
document.write( "Choice C: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2F59049%29%289%5E4%29%283%29%28-3%29+=+4 ALIGN=MIDDLE  ALT=\"%28-4%2F59049%29%289%5E4%29%283%29%28-3%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Choice E: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2F729%29%289%5E2%29%283%29%28-3%29+=+4 ALIGN=MIDDLE  ALT=\"%28-4%2F729%29%289%5E2%29%283%29%28-3%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Choice F: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2F243%29%289%29%283%5E2%29%28-3%29+=+4 ALIGN=MIDDLE  ALT=\"%28-4%2F243%29%289%29%283%5E2%29%28-3%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: C, E, and F are all polynomials that satisfy all of the given conditions.<br><BR>\n" );
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