document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155245>Question 155245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for what value(s) of k will the graph of y = x^2-3x+k \r<BR>\n" );
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document.write( "a) touch the x-axis\r<BR>\n" );
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document.write( "b) never meet 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 #114305 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=114305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) \r<BR>\n" );
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document.write( "It will touch the x-axis when the polynomial has only one solution. If the polynomial has only one solution, then the discriminant is equal to zero. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=b%5E2-4ac ALIGN=MIDDLE  ALT=\"D=b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the discriminant formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28-3%29%5E2-4%281%29%28k%29 ALIGN=MIDDLE  ALT=\"0=%28-3%29%5E2-4%281%29%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=0 ALIGN=MIDDLE  ALT=\"D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3 ALIGN=MIDDLE  ALT=\"b=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=k ALIGN=MIDDLE  ALT=\"c=k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=9-4%281%29%28k%29 ALIGN=MIDDLE  ALT=\"0=9-4%281%29%28k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -3 to get 9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=9-4k ALIGN=MIDDLE  ALT=\"0=9-4k\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9=-4k ALIGN=MIDDLE  ALT=\"-9=-4k\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 9 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F4=k ALIGN=MIDDLE  ALT=\"9%2F4=k\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -4\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=9%2F4 ALIGN=MIDDLE  ALT=\"k=9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the polynomial will have only one solution and will touch the x-axis.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "Follow the same procedure described above, but this time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%3C0 ALIGN=MIDDLE  ALT=\"D%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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