document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172128>Question 172128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph and give the coordinates of the vertex,x and y intercepts, and graph\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=f%28x%29=-x%5E2-6x ALIGN=MIDDLE  ALT=\"y=f%28x%29=-x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130897 by </B><A HREF=/tutors/aboutme.mpl?userid=EMStelley><B>EMStelley(208)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EMStelley><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=EMStelley><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to find the vertex (h,k), the easiest way is to use the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"h=-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So here, a=-1, b=-6, and c=0, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-%28-6%29%2F%282%28-1%29%29=6%2F%28-2%29=-3 ALIGN=MIDDLE  ALT=\"h=-%28-6%29%2F%282%28-1%29%29=6%2F%28-2%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find k, you just evaluate the function at x=-3.  So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=-%28%28-3%29%5E2%29-6%28-3%29=-9%2B18=9 ALIGN=MIDDLE  ALT=\"f%28-3%29=-%28%28-3%29%5E2%29-6%28-3%29=-9%2B18=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the vertex is (-3,9).  The y intercept is found by setting x equal to 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=-0%5E2-6%280%29=0 ALIGN=MIDDLE  ALT=\"f%280%29=-0%5E2-6%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the y intercept is the origin, (0,0).<BR>\n" );
document.write( "The x intercepts are found by setting y = 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-x%5E2-6x ALIGN=MIDDLE  ALT=\"0=-x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factoring, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%28-x-6%29 ALIGN=MIDDLE  ALT=\"0=x%28-x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-6=0 ALIGN=MIDDLE  ALT=\"-x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So our two x intercepts are at x=0 and x=-6.<BR>\n" );
document.write( "Finally, graphing, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C+-10%2C10%2C-10%2C10%2C-x%5E2-6x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C+-10%2C10%2C-10%2C10%2C-x%5E2-6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );