document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=766277>Question 766277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the following for the function f(x)=(x+6)^2 (x-3)^2.<BR>\n" );
document.write( "a) Find the x- and y- intercepts of the polynomial function f.<BR>\n" );
document.write( "b) Determine whether the graph of f crosses or touches the x-axis at each x-intercept.<BR>\n" );
document.write( "c)Put all the information together to obtain the graph of f.\r<BR>\n" );
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document.write( "The x-intercepts is(are)___________<BR>\n" );
document.write( "The y-intercept of f is___________.\r<BR>\n" );
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document.write( "Does the graph cross or touch the x-axis at the smaller x-intercept?<BR>\n" );
document.write( "a) The graph touches the x-axis.<BR>\n" );
document.write( "b) the graph crosses the x-axis.\r<BR>\n" );
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document.write( "Does the graph cross or touch the x-axis at the larger x-intercept?<BR>\n" );
document.write( "a)the graph touches the x-axis.<BR>\n" );
document.write( "b)the graph crosses the x-axis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466837 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=466837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Some limited help...\r<BR>\n" );
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document.write( "Two zeros are -6 and +3.  This means f(-6)=0 and f(3)=0, so you have x intercepts of (-6,0) and (3,0).\r<BR>\n" );
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document.write( "Vertical axis intercept?  Try y=(0+6)^2(0-3)^2=36*9=324.<BR>\n" );
document.write( "y-intercept is (0,324).\r<BR>\n" );
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document.write( "Check sign of f in the three intervals.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-6 ALIGN=MIDDLE  ALT=\"x%3C-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f=(-)^2 *(-)^2=(+) positive<BR>\n" );
document.write( "In fact, look at this function!  Each binomial factor is squared.  This function will be positive everywhere.  Not necessary to check in the other two intervals.\r<BR>\n" );
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document.write( "Because the graph has TWO zeros, and is POSITIVE everywhere, the graph will TOUCH but not cross below the x-axis at (-6,0) and (3,0).  \r<BR>\n" );
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