document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081057>Question 1081057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i graph the parabola (y-9)^2=12(x-8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695151 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=695151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That is a modified form of the parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You probably know that the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-3%2C27%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-3%2C27%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Nice graph, symmetrical about the positive y-axis (the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > line),<BR>\n" );
document.write( "with a vertex at point (0,0), the origin.<BR>\n" );
document.write( "Each point has a twin that is its reflection about the y-axis,<BR>\n" );
document.write( "except the vertex.<BR>\n" );
document.write( "The vertex is a unique point, and its reflection is the vertex itself.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you swap the x for the y and the y for the x, you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=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=graph%28300%2C300%2C-3%2C27%2C-5%2C5%2Csqrt%28x%29%2C-sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C27%2C-5%2C5%2Csqrt%28x%29%2C-sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Nice graph, symmetrical about the positive x-axis,<BR>\n" );
document.write( "with a vertex at point (0,0), the origin.<BR>\n" );
document.write( "Points with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28y%29=1 ALIGN=MIDDLE  ALT=\"abs%28y%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=1 ALIGN=MIDDLE  ALT=\"y%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "have <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;\" > .<BR>\n" );
document.write( "Points with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28y%29=2 ALIGN=MIDDLE  ALT=\"abs%28y%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=4 ALIGN=MIDDLE  ALT=\"y%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you graphed them on wax paper (or anything translucent enough),<BR>\n" );
document.write( "flipping the paper so as to swap the arrows for the x- and y-axes<BR>\n" );
document.write( "would turn one graph into the other.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-8%29=%28y-9%29%5E2 ALIGN=MIDDLE  ALT=\"12%28x-8%29=%28y-9%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a version of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with a vertex at (8,9) ,<BR>\n" );
document.write( "the unique point with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x-8=0%2Cy-9=0%29 ALIGN=MIDDLE  ALT=\"system%28x-8=0%2Cy-9=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=8%2Cy=9%29 ALIGN=MIDDLE  ALT=\"system%28x=8%2Cy=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Points with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28y-9%29=1 ALIGN=MIDDLE  ALT=\"abs%28y-9%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-9%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-9%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10 ALIGN=MIDDLE  ALT=\"y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8 ALIGN=MIDDLE  ALT=\"y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-8%29=1 ALIGN=MIDDLE  ALT=\"12%28x-8%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8=1%2F12 ALIGN=MIDDLE  ALT=\"x=8=1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Points with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28y-9%29=2 ALIGN=MIDDLE  ALT=\"abs%28y-9%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-9%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28y-9%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=11 ALIGN=MIDDLE  ALT=\"y=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7 ALIGN=MIDDLE  ALT=\"y=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x-8%29=4 ALIGN=MIDDLE  ALT=\"12%28x-8%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8=%281%2F12%294 ALIGN=MIDDLE  ALT=\"x=8=%281%2F12%294\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "So, the graph is like the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "except it has been moved up and right to shift the vertex to (8,9),<BR>\n" );
document.write( "its axis of symmetry is now the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9 ALIGN=MIDDLE  ALT=\"y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and it has been shrunk along the x-direction by a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so you go much farther from the vertex in the x-direction<BR>\n" );
document.write( "and get the same distance away from its <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28y=9%29 ALIGN=MIDDLE  ALT=\"blue%28y=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > axis of symmetry:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C6%2Cy%2C7%2C8%2C9%2C10%2C11%2C%0D%0Ax-8%2C1%2F14%2F12=1%2F3%2C1%2F12%2C0%2C1%2F12%2C1%2F3%2C%0D%0Ax%2C8%261%2F3%2C8%261%2F12%2C8%2C8%261%2F12%2C8%261%2F3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28150%2C450%2C-6%2C24%2C-6%2C24%2C9%2Bsqrt%2812%28x-8%29%29%2C9-sqrt%2812%28x-8%29%29%2C9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );