document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=376362>Question 376362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the graph of the function f(x)=x^2-kx+k+8 touches the x-axis at one point. what are the possible values of k?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks in advance!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #267805 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=267805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since<BR>\n" );
document.write( "f(x)=x^2-kx+k+8<BR>\n" );
document.write( "touches the x-axis at only one point, it must be the vertex.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "this must mean the \"determinant\" is zero:<BR>\n" );
document.write( "b^2-4ac = 0<BR>\n" );
document.write( "(-k)^2 - 4(1)(k+8) = 0<BR>\n" );
document.write( "(-k)^2 - 4(k+8) = 0<BR>\n" );
document.write( "k^2 - 4k-32 = 0<BR>\n" );
document.write( "(k-8)(k+4) = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "k = {-4, 8}\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );