document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912790>Question 912790</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I want to know how you workout the eqaution for a parabola line but the vertex isn't on the y-axis and how to change the width of the line. Thank in advanced. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554062 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=554062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can move the parabola either right<BR>\n" );
document.write( "or left by writing equation as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28+x+-+a+%29%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+%28+x+-+a+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+x%5E2+-+2ax+%2B+a%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+x%5E2+-+2ax+%2B+a%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Notice that <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;\" > when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+%28+a+-+a+%29%5E2+ ALIGN=MIDDLE  ALT=\"+0+=+%28+a+-+a+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is at (a,0)<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "This is how you move the vertex from<BR>\n" );
document.write( "(0,0) to anywhere on the x-axis<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Then, in order to move up or down,<BR>\n" );
document.write( "you need:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28+x-a+%29%5E2+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+%28+x-a+%29%5E2+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "To make the parabola narrower ( skinny ),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+c%2A%28+x-a+%29%5E2+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+c%2A%28+x-a+%29%5E2+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%3E1+ ALIGN=MIDDLE  ALT=\"+c%3E1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To make the parabola wider ( fatter ),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+%3C1+ ALIGN=MIDDLE  ALT=\"+c+%3C1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Say<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+3+ ALIGN=MIDDLE  ALT=\"+a+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+5+ ALIGN=MIDDLE  ALT=\"+b+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+1+ ALIGN=MIDDLE  ALT=\"+c+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "A 2nd parabola is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+3+ ALIGN=MIDDLE  ALT=\"+a+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-5+ ALIGN=MIDDLE  ALT=\"+b+=+-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+4+ ALIGN=MIDDLE  ALT=\"+c+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here are the plots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-3%2C+10%2C+-7%2C+10%2C+%28+x+-+3+%29%5E2+-+5%2C+4%2A%28+x+-+3+%29%5E2+-+5+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The skinnier one is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+4%2A%28+x-3+%29%5E2+-+5+ ALIGN=MIDDLE  ALT=\"+y+=+4%2A%28+x-3+%29%5E2+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hope this helps\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );