document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79487>Question 79487</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131339982/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, give the center and foci. Sketch the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E2-x-6y%2B5=0 ALIGN=MIDDLE  ALT=\"3y%5E2-x-6y%2B5=0\"   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 #57046 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20059)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, give the center and foci. Sketch the graph.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E2-x-6y%2B5=0 ALIGN=MIDDLE  ALT=\"3y%5E2-x-6y%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "It is a parabola because it only has ONE squared letter.\r<BR>\n" );
document.write( "\n" );
document.write( "Get all the terms in the squared letter on the left and <BR>\n" );
document.write( "all other terms on the right:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E2-6y=x-5 ALIGN=MIDDLE  ALT=\"3y%5E2-6y=x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Factor out the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y%5E2-2y%29+=+x-5 ALIGN=MIDDLE  ALT=\"3%28y%5E2-2y%29+=+x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Complete the square by adding 1 inside the parentheses<BR>\n" );
document.write( "on the left.  However note that when we placing a 1 <BR>\n" );
document.write( "inside the parentheses on the left, we are really adding 3<BR>\n" );
document.write( "because of the 3 multiplier in front of the parentheses<BR>\n" );
document.write( "so we must add 3 to the right side to offset.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y%5E2-2y%2B1%29+=+x-5%2B3 ALIGN=MIDDLE  ALT=\"3%28y%5E2-2y%2B1%29+=+x-5%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Factor the trinomial on the left side as a perfect square,<BR>\n" );
document.write( "and combine terms on the right:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y-1%29%5E2+=+x-2 ALIGN=MIDDLE  ALT=\"3%28y-1%29%5E2+=+x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%293%28y-1%29%5E2+=+%281%2F3%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%281%2F3%293%28y-1%29%5E2+=+%281%2F3%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%28y-1%29%5E2+=+%281%2F3%29%28x-2%29 ALIGN=MIDDLE  ALT=\"1%28y-1%29%5E2+=+%281%2F3%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-1%29%5E2+=+%281%2F3%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%28y-1%29%5E2+=+%281%2F3%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now the equation is in the form:\r<BR>\n" );
document.write( "\n" );
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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "where the vertex is (h,k) = (2,1)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C167%2C+-2%2C7%2C-2%2C3%2C0%2C0%2C1%2Bsqrt%28%28x-2%29%2F3%29%2C0%2C0%2C0%2C1-sqrt%28%28x-2%29%2F3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );