document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980451>Question 980451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> vertex: ?<BR>\n" );
document.write( "focus point: ?<BR>\n" );
document.write( "equation of the axis of symmetry: ?<BR>\n" );
document.write( "equation of directrix: ?<BR>\n" );
document.write( "2 random points on equation: ? \r<BR>\n" );
document.write( "\n" );
document.write( "y^2 + 8x + 8 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601606 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=601606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Best thing is use the derived equation for parabola translated from standard position,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=4px ALIGN=MIDDLE  ALT=\"y%5E2=4px\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2=4p%28x-h%29 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2=4p%28x-h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which the vertex is (h,k).  The distance from vertex to either focus or directrix is absolute value of p.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B8=-y%5E2 ALIGN=MIDDLE  ALT=\"8x%2B8=-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28x%2B1%29=-y%5E2 ALIGN=MIDDLE  ALT=\"8%28x%2B1%29=-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%28x%2B1%29=y%5E2 ALIGN=MIDDLE  ALT=\"-8%28x%2B1%29=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is concave to the left and has vertex (-1,0).<BR>\n" );
document.write( "Axis of symmetry is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8=4p ALIGN=MIDDLE  ALT=\"-8=4p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-2 ALIGN=MIDDLE  ALT=\"p=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Meaning the focus and directrix are both two units away from the point (-1,0).  Focus must be on the concave side, so  (-3,0) is the focus, and  (1,0) is a point on the directrix.  Directrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );