document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636499>Question 636499</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=x2 + 2x - 9\r<BR>\n" );
document.write( "\n" );
document.write( "determine whether the given quadratic function has a minmum or maximun value. then find the coordinated of the mininmun or maximun point. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401058 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=401058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E2+%2B+2x+-+9+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E2+%2B+2x+-+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the coefficient of the squared term is positive<BR>\n" );
document.write( "( +1 ), then the function has a minimum.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "The  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > value of the minimum will <BR>\n" );
document.write( "be at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b+%2F+%282a%29+ ALIGN=MIDDLE  ALT=\"+-b+%2F+%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the <BR>\n" );
document.write( "equation is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-2+%2F+%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-2+%2F+%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2+%2F+%282%2A1%29+=+-1+ ALIGN=MIDDLE  ALT=\"+-2+%2F+%282%2A1%29+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Plug this back into the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%281%29+=+%28-1%29%5E2+%2B+2%2A%28-1%29+-+9+ ALIGN=MIDDLE  ALT=\"+f%281%29+=+%28-1%29%5E2+%2B+2%2A%28-1%29+-+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%281%29+=+1+-+2+-+9+ ALIGN=MIDDLE  ALT=\"+f%281%29+=+1+-+2+-+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%281%29+=+-10+ ALIGN=MIDDLE  ALT=\"+f%281%29+=+-10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "So the minimum is at (-1,-10)<BR>\n" );
document.write( "Here's a plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-20%2C+10%2C+x%5E2+%2B+2x+-+9%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-20%2C+10%2C+x%5E2+%2B+2x+-+9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );