document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195766>Question 195766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One last problem I'm having trouble with requires that I dtermine the co-ordinates of the lowest (minimum point on the curve)<BR>\n" );
document.write( "y(x) = -8x - 7 - x^2.<BR>\n" );
document.write( "I also need to prove the point is minimum.\r<BR>\n" );
document.write( "\n" );
document.write( "Any help please.\r<BR>\n" );
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document.write( "Thanks, -nick </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146800 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=146800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  dtermine the co-ordinates of the lowest (minimum point on the curve)<BR>\n" );
document.write( "y(x) = -8x - 7 - x^2.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2 + 8x = -y+7<BR>\n" );
document.write( "Complete the square:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x^2 + 8x + 16 = -y + 23<BR>\n" );
document.write( "(x+4)^2 = -y + 23<BR>\n" );
document.write( "y = -(x+4)^2 + 23<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "The vertex occurs at (-4,23)<BR>\n" );
document.write( "The vertex is not the minimum point, it is the maximum point.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-20%2C20%2C-10%2C30%2C-%28x%2B4%29%5E2+%2B+23%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-20%2C20%2C-10%2C30%2C-%28x%2B4%29%5E2+%2B+23%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );