document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178187>Question 178187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Does this function have a maximum or a minimum?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-5=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > After solving this equation I came up with (x=1) and (x=-5). Am I correct? Please include details. I don't yet know how to find a max or min. Please explain how to find this answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133184 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=133184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-5=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Simply by looking at the coefficient associated with the 'x^2' term (in this case, it's a POSITIVE 1) you can immediately tell that you will find the MINIMUM by finding the \"vertex\" or x-axis of symmetry.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A quadratic forms a parabola -- either it is \"open upward\" or \"open downward\".  If it is \"open upward\" the vertex is at the minimum.  If is \"open downward\" the vertex is at a maximum.  If the coefficient (associated with the x^2) is POSITIVE -- it is \"open upward\" (think of it this way, if you're POSITIVE you would have a happy face).  If the coefficient is NEGATIVE -- it is \"open downward\" (if you're NEGATIVE, you would be sad faced).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The \"vertex form\" is:<BR>\n" );
document.write( "y= a(x-h)^2+k<BR>\n" );
document.write( "where (h,k) is the vertex<BR>\n" );
document.write( ". <BR>\n" );
document.write( "To find the vertex, complete the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-5 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%29-5 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%29-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%2B4%29-5-4 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%2B4%29-5-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%2B4%29-9 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%2B4%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=%28x%2B2%29%5E2-9 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(h,k) = (-2, -9) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );