document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316771>Question 316771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me. State whether the vertex of the function is a maximum or minimum and give the corresponsing maximum or minimum value of the function.\r<BR>\n" );
document.write( "\n" );
document.write( "f(x)= x square + 14x+47 \r<BR>\n" );
document.write( "\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226735 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=226735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First convert to vertex form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, by completing the square.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B14x%2B47 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B14x%2B47\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2B14x%2B49%29-2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B14x%2B49%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B7%29%5E2-2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B7%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is located at (-7,-2).<BR>\n" );
document.write( "Since the coefficient for the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is positive, the parabola opens upwards, and the vertex is a minimum. <BR>\n" );
document.write( "The minimum value occurs at the vertex.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ymin=-2 ALIGN=MIDDLE  ALT=\"ymin=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+300%2C300%2C+-15%2C+5%2C+-10%2C+10%2Cgrid%281%29%2Ccircle%28-7%2C-2%2C.3%29%2C+graph%28+300%2C300%2C+-15%2C+5%2C+-10%2C+10%2C+x%5E2%2B14x%2B47%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );