document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=865756>Question 865756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the following for the function f(x)=(x+4)^2(x-2)^2<BR>\n" );
document.write( "a. find the x and y intercepts<BR>\n" );
document.write( "b.determine whether the graph of f crosses or touches the x-axis at each untercept<BR>\n" );
document.write( "c.put all the information together to obtain graph of f<BR>\n" );
document.write( "thanks in advance for the help<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521848 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=521848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B4%29%5E2%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B4%29%5E2%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is already in factored form.  x intercepts are -4 and +2.<BR>\n" );
document.write( "y-intercept happens for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%280%29%29=4%5E2%2A2%5E2=16%2A4=highlight%2864%29 ALIGN=MIDDLE  ALT=\"highlight%28f%280%29%29=4%5E2%2A2%5E2=16%2A4=highlight%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Examine the function factors very carefully.  Each individual binomial factor may be less than, equal to, or greater than zero; but because both factors are squared, f(x) stays POSITIVE, so will always be at or above the horizontal axis.  This means, f(x) NEVER crosses the x axis at any x intercept.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The vertical labeling is imprecise, but here is a fair representation of the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-7%2C5%2C-5%2C80%2C%28x%2B4%29%5E2%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-7%2C5%2C-5%2C80%2C%28x%2B4%29%5E2%28x-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );