document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177687>Question 1177687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe, sketch and label the focus, vertex, and directrix of the parabola 4𝑦² + 8𝑦 − 8𝑥 + 7 = 0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806796 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20855)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=806796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2+%2B+8y+%E2%88%92+8x+%2B+7+=+0 ALIGN=MIDDLE  ALT=\"4y%5E2+%2B+8y+%E2%88%92+8x+%2B+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284y%5E2+%2B+8y+%29=8x+-+7+ ALIGN=MIDDLE  ALT=\"%284y%5E2+%2B+8y+%29=8x+-+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y%5E2+%2B+2y+%29=8x+-+7+ ALIGN=MIDDLE  ALT=\"4%28y%5E2+%2B+2y+%29=8x+-+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+%2B+2y+%29=2x+-+7%2F4 ALIGN=MIDDLE  ALT=\"%28y%5E2+%2B+2y+%29=2x+-+7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .........complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+%2B+2y+%2Bb%5E2%29-b%5E2=2x+-+7%2F4 ALIGN=MIDDLE  ALT=\"%28y%5E2+%2B+2y+%2Bb%5E2%29-b%5E2=2x+-+7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........b=2/2=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+%2B+2y+%2B1%5E2%29-1%5E2=2x+-+7%2F4 ALIGN=MIDDLE  ALT=\"%28y%5E2+%2B+2y+%2B1%5E2%29-1%5E2=2x+-+7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2-1=2x+-+7%2F4 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2-1=2x+-+7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2=2x+-+7%2F4%2B1 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2=2x+-+7%2F4%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2=2x+-+3%2F4 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2=2x+-+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2=2%28x+-+%283%2F4%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2=2%28x+-+%283%2F4%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2=2%28x+-+3%2F8%29 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2=2%28x+-+3%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so you have\r<BR>\n" );
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document.write( "<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;\" >is the standard equation for a right-left facing parabola with vertex at  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+ ALIGN=MIDDLE  ALT=\"+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" >), \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2=2%28x-3%2F8%29 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2=2%28x-3%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3%2F8 ALIGN=MIDDLE  ALT=\"h=3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-1 ALIGN=MIDDLE  ALT=\"k=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p=2+ ALIGN=MIDDLE  ALT=\"4p=2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1%2F2 ALIGN=MIDDLE  ALT=\"p=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "vertex: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "focus:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Bp ALIGN=MIDDLE  ALT=\"h%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F8 ALIGN=MIDDLE  ALT=\"7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "directrix: \r<BR>\n" );
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document.write( "parabola is symmetric around the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-axis and so the directrix is a line parallel to the y-axis, a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p ALIGN=MIDDLE  ALT=\"-p\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the vertex ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) x-coordinate \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F8-p ALIGN=MIDDLE  ALT=\"x=3%2F8-p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1%2F2 ALIGN=MIDDLE  ALT=\"p=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F8-1%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F8-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F8-4%2F8 ALIGN=MIDDLE  ALT=\"x=3%2F8-4%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F8 ALIGN=MIDDLE  ALT=\"x=-1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%283%2F8%2C-1%2C.12%29%2C+locate%283%2F8%2C-1%2CV%283%2F8%2C-1%29%29%2C%0D%0Acircle%287%2F8%2C-1%2C.12%29%2C+locate%287%2F8%2C-0.3%2CF%287%2F8%2C-1%29%29%2C%0D%0Agreen%28line%28-1%2F8%2C-10%2C-1%2F8%2C10%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C-sqrt%282%28x+-+3%2F8%29%29-1%2C+sqrt%282%28x+-+3%2F8%29%29-1%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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