document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=434359>Question 434359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the quadratic relation ship between x and y\r<BR>\n" );
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document.write( "1x   3y\r<BR>\n" );
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document.write( "2    12y \r<BR>\n" );
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document.write( "4x   48y\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300961 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=300961\">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=y+=+3x%5E2 ALIGN=MIDDLE  ALT=\"y+=+3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To show this, Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+a%281-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"3+=+a%281-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+a%282-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"12+=+a%282-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48+=+a%284-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"48+=+a%284-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtracting the 1st from the 2nd, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+a%282-h%29%5E2+-+a%281-h%29%5E2 ALIGN=MIDDLE  ALT=\"9+=+a%282-h%29%5E2+-+a%281-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> 9 = 3a - 2ah <BR>\n" );
document.write( "Subtracting the 2nd from the 3rd, we get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=+a%284-h%29%5E2+-+a%282-h%29%5E2 ALIGN=MIDDLE  ALT=\"36=+a%284-h%29%5E2+-+a%282-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> 36 = 12a - 4ah, or 9 = 3a - ah.\r<BR>\n" );
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document.write( "Now we have the equations 9 = 3a - 2ah, and 9 = 3a - ah.<BR>\n" );
document.write( "subtracting the first from the second, we get ah = 0.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E0 ALIGN=MIDDLE  ALT=\"a%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have h = 0.<BR>\n" );
document.write( "Substituting h = 0 into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+a%281-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"3+=+a%281-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+=+a%282-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"12+=+a%282-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get<BR>\n" );
document.write( "3 = a + k and 12 = 4a + k.<BR>\n" );
document.write( "From this we get a = 3.<BR>\n" );
document.write( "Finally putting h = 0 and a = 3 into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+a%281-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"3+=+a%281-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get k = 0. </SPAN>\n" );
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