document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=621035>Question 621035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the coordinates of the vertex and foci, and what is the equation for the directrix of the following parabolic equations?\r<BR>\n" );
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document.write( "a. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2+=+-8%2A%28y%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2+=+-8%2A%28y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-1%29%5E2+=+16x ALIGN=MIDDLE  ALT=\"%28y-1%29%5E2+=+16x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+4%2A%28y-4%29 ALIGN=MIDDLE  ALT=\"x%5E2+=+4%2A%28y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B6%29%5E2+=+-12%2A%28x-1%29 ALIGN=MIDDLE  ALT=\"%28y%2B6%29%5E2+=+-12%2A%28x-1%29\"   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 #393182 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=393182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What are the coordinates of the vertex and foci, and what is the equation for the directrix of the following parabolic equations? <BR>\n" );
document.write( "a. (x+2)^2 = -8*(y+3)<BR>\n" );
document.write( "This is an equation of a parabola that opens downwards<BR>\n" );
document.write( "Form of equation: (x-h)^2=-4p(y-k)<BR>\n" );
document.write( "vertex:(-2,-3)<BR>\n" );
document.write( "axis of symmetry: x=-2<BR>\n" );
document.write( "4p=8<BR>\n" );
document.write( "p=2<BR>\n" );
document.write( "focus: (-2,-3-p)=(-2,-3-2)=(-2,-5) (p units below vertex on the axis of symmetry)<BR>\n" );
document.write( "directrix: y=-1  (p units above vertex on the axis of symmetry)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b. (y-1)^2 = 16x<BR>\n" );
document.write( "This is an equation of a parabola that opens rightwards<BR>\n" );
document.write( "Form of equation: (y-k)^2=4p(x-h)<BR>\n" );
document.write( "vertex:(0,1)<BR>\n" );
document.write( "axis of symmetry: y=1<BR>\n" );
document.write( "4p=16<BR>\n" );
document.write( "p=4<BR>\n" );
document.write( "focus: (0+p,1)=(0+4,1)=(4,1) (p units right of vertex on the axis of symmetry)<BR>\n" );
document.write( "directrix: x=-4  (p units left of vertex on the axis of symmetry)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c. x^2 = 4*(y-4)<BR>\n" );
document.write( "This is an equation of a parabola that opens upwards<BR>\n" );
document.write( "Form of equation: (x-h)^2=4p(y-k)<BR>\n" );
document.write( "vertex:(0,4)<BR>\n" );
document.write( "axis of symmetry: x=0<BR>\n" );
document.write( "4p=4<BR>\n" );
document.write( "p=2<BR>\n" );
document.write( "focus: (0,4+p)=(0,4+2)=(0,6) (p units above vertex on the axis of symmetry)<BR>\n" );
document.write( "directrix: y=2  (p units below vertex on the axis of symmetry)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "d. (y+6)^2 = -12*(x-1)<BR>\n" );
document.write( "This is an equation of a parabola that opens leftwards<BR>\n" );
document.write( "Form of equation: (y-k)^2=-4p(x-h)<BR>\n" );
document.write( "vertex:(1,-6)<BR>\n" );
document.write( "axis of symmetry: y=-6<BR>\n" );
document.write( "4p=12<BR>\n" );
document.write( "p=3<BR>\n" );
document.write( "focus: (1-p,-6)=(1- 3,-6)=(-2,-6) (p units left of vertex on the axis of symmetry)<BR>\n" );
document.write( "directrix: x=4  (p units right of vertex on the axis of symmetry)<BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );