document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515337>Question 515337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the vertex, the line of symetry, the minumum/maximum value of the quadratic function and graph.  -(x+5)^2-6<BR>\n" );
document.write( "vertex=<BR>\n" );
document.write( "line of symetry=<BR>\n" );
document.write( "min/max=<BR>\n" );
document.write( "is it min or max=<BR>\n" );
document.write( "graph=<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343914 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=343914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -(x+5)^2 -6 = -(x+5)(x+5) -6 = -(x^2 +10x + 25) -6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-(x^2 +10x + 25) -6 = -x^2 -10x -25 -6 = -x^2 -10x -31<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The graph will help orient us to the solution<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28500%2C500%2C-12%2C5%2C-12%2C5%2C-x%5E2+-10%2Ax+-31%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-12%2C5%2C-12%2C5%2C-x%5E2+-10%2Ax+-31%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The vertex has a x value of -b/2a = -(-10)/(-2*1) = -5<BR>\n" );
document.write( "When x=-5<BR>\n" );
document.write( "y = -x^2 -10x -31<BR>\n" );
document.write( "y = -25 +50 -31<BR>\n" );
document.write( "y = -6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The vertex = (-5,-6).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The line of symmetry is x=-5, a vertical line.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the parabola opens 'down' we know the vertex is the maximum.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We also know this from the graph.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And we can apply calculus to set the first derivative = 0.<BR>\n" );
document.write( "dy/dx = -2x -10 = 0<BR>\n" );
document.write( "2x = -10<BR>\n" );
document.write( "x = -5<BR>\n" );
document.write( "Correct.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );