document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=747568>Question 747568</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complete the square as an aid in graphing: y = x^2 + 4x - 2\r<BR>\n" );
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document.write( "After completed the square, graph the parabola.\r<BR>\n" );
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document.write( "Please show all work so I can understand. \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454989 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=454989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of the parabola given in general form does not make graphing into any easy process.  Completing the Square and converting to standard form does make graphing much easier to do.\r<BR>\n" );
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document.write( "The trinomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-2 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > contains an expression which is like the area of a rectangle and a term can be added to turn this expression into a factorable square expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B4x-2 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B4x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2%2B4x%29-2 ALIGN=MIDDLE  ALT=\"y=%28x%5E2%2B4x%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we want to add a square term to the grouped expression, and this term will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F2%29%5E2=4 ALIGN=MIDDLE  ALT=\"%284%2F2%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  We also must subtract the same term.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2%2B4x%2B4%29-2-4 ALIGN=MIDDLE  ALT=\"y=%28x%5E2%2B4x%2B4%29-2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%28x%2B2%29%5E2-6%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%28x%2B2%29%5E2-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--------STANDARD FORM.<BR>\n" );
document.write( "Compare to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which the vertex is (h,k) and is a minimum.  If it were as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=-%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the vertex would be a maximum.\r<BR>\n" );
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document.write( "Vertex is (-2,-6), and this vertex is the parabola's minimum.  You can find the zeros using the general solution to quadratic formula, or you could choose to solve for x starting from your standard form equation just found. </SPAN>\n" );
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