document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=331594>Question 331594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please write the quadratic function in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"f%28x%29=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > by the COMPLETING THE SQUARE METHOD. Please then identify the vertex.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=x%5E2%2B4x%2B5 ALIGN=MIDDLE  ALT=\"h%28x%29=x%5E2%2B4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #237674 by </B><A HREF=/tutors/aboutme.mpl?userid=texttutoring><B>texttutoring(324)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=texttutoring><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=texttutoring><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=237674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To complete the square, you need to halve the b term (b=4 in your question) and then square it. Half of b=4 is 2. Square it and you will get 4 again. Now add 4:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 + 4x + 4  + 5 - 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice that I also subtracted 4 at the end. This is because you are not just allowed to add 4 to the equation, you can only add zero. You achieve this by subtracting the same number afterwards. Now x^2+4x +4 can be turned into a perfect square:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=(x^2 + 4x + 4)  + 5 - 4<BR>\n" );
document.write( "=(x+2)^2 +1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now it is in the form you want. The vertex is (-2,1). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );