document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044783>Question 1044783</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation <BR>\n" );
document.write( "Find the Parabola properties and graph<BR>\n" );
document.write( "x^2+4x+2y=0\r<BR>\n" );
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document.write( "Vertex:<BR>\n" );
document.write( "Focus:<BR>\n" );
document.write( "Directrix:<BR>\n" );
document.write( "Axis of symmetry:<BR>\n" );
document.write( "Endpoints of latus retum:\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 #660168 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=660168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 +4x +2y = 0<BR>\n" );
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document.write( "y = (-x^2/2) -2x<BR>\n" );
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document.write( "This is a parabola that curves downward<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+1%2C+-2%2C+3%2C+%28-x%5E2%2F2%29+-2x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+1%2C+-2%2C+3%2C+%28-x%5E2%2F2%29+-2x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the x coordinate of the vertex is defined<BR>\n" );
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document.write( "x = -b/2a = -(-2) / (2(-1/2)) = -2<BR>\n" );
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document.write( "y = (-2^2/2) -2(-2) = 2<BR>\n" );
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document.write( "vertex is (-2,2)     <BR>\n" );
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document.write( "y = (-x^2/2) -2x<BR>\n" );
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document.write( "2y = -x^2 -4x<BR>\n" );
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document.write( "-2y = x^2 +4x<BR>\n" );
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document.write( "Complete the square<BR>\n" );
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document.write( "-2y +4 = (x+2)^2<BR>\n" );
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document.write( "This is the standard form equation for our parabola<BR>\n" );
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document.write( "-2(y-2) = (x+2)^2<BR>\n" );
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document.write( "note that 4p = -2, h = -2, k = 2<BR>\n" );
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document.write( "4p = -2<BR>\n" );
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document.write( "p = -1/2<BR>\n" );
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document.write( "Focus = (-2, 2-(1/2)) = (-2, 1.5)<BR>\n" );
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document.write( "Directrix = 2-(-1/2) = 2.5<BR>\n" );
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document.write( "axis of symmetry is x = -2<BR>\n" );
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