document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=453215>Question 453215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the vertex of the given equation. Parabolas.<BR>\n" );
document.write( "y = -x2 + 5x - 6<BR>\n" );
document.write( "Can you help me please! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #311410 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=311410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form of a parabola is given by the equation:\r<BR>\n" );
document.write( "\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=Ax%5E2+%2B+Bx+%2B+C++ ALIGN=MIDDLE  ALT=\"y=Ax%5E2+%2B+Bx+%2B+C++\"   DISABLED_style= \"max-width:90%; height:auto;\" >where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > are arbitrary <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=real+ ALIGN=MIDDLE  ALT=\"real+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=constants ALIGN=MIDDLE  ALT=\"constants\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   DISABLED_style= \"max-width:90%; height:auto;\" > is  at: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-B%2F2A+ ALIGN=MIDDLE  ALT=\"+-B%2F2A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+-+B%5E2%2F4A ALIGN=MIDDLE  ALT=\"C+-+B%5E2%2F4A\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
document.write( "\n" );
document.write( "you are given:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2+%2B+5x+-+6 ALIGN=MIDDLE  ALT=\"y+=+-x%5E2+%2B+5x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is already in general form of a parabola\r<BR>\n" );
document.write( "\n" );
document.write( "so, <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=5 ALIGN=MIDDLE  ALT=\"B=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-6 ALIGN=MIDDLE  ALT=\"C=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "now find the coordinates of the vertex:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-B%2F2A+ ALIGN=MIDDLE  ALT=\"+-B%2F2A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+-+B%5E2%2F4A ALIGN=MIDDLE  ALT=\"C+-+B%5E2%2F4A\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-B%2F2A=-5%2F2%28-1%29=-5%2F-2=5%2F2=2.5+ ALIGN=MIDDLE  ALT=\"+-B%2F2A=-5%2F2%28-1%29=-5%2F-2=5%2F2=2.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+-+B%5E2%2F4A=%28-6%29-25%2F4%28-1%29=-6%2B25%2F4=-6%2B6.25=0.25 ALIGN=MIDDLE  ALT=\"C+-+B%5E2%2F4A=%28-6%29-25%2F4%28-1%29=-6%2B25%2F4=-6%2B6.25=0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "so, the vertex is at: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5 ALIGN=MIDDLE  ALT=\"2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25 ALIGN=MIDDLE  ALT=\"0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+-x%5E2+%2B+5x+-+6%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+-x%5E2+%2B+5x+-+6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );