document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=889601>Question 889601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of the parabola with vertex on the line y=x, the axis of parabola is parallel to the x-axis and passing through (6,-2)and (3,4)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538381 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39627)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=538381\">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=highlight_green%28x=a%28y-k%29%5E2%2Bh%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x=a%28y-k%29%5E2%2Bh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, parabola parallel to the horizontal axis.\r<BR>\n" );
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document.write( "The line y=x containing the vertex means that the two coordinates of this point are equal in value.<BR>\n" );
document.write( "Call this vertex (n,n).<BR>\n" );
document.write( "The equation of the parabola can be expressed, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x=a%28y-n%29%5E2%2Bn%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x=a%28y-n%29%5E2%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The variables, once the given points are substituted, will be a and n.  General form should give<BR>\n" );
document.write( "a system of equations which we could solve for a and n.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a%28y%5E2-2yn%2Bn%5E2%29%2Bn ALIGN=MIDDLE  ALT=\"x=a%28y%5E2-2yn%2Bn%5E2%29%2Bn\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=ay%5E2-2ayn%2Ban%5E2%2Bn ALIGN=MIDDLE  ALT=\"x=ay%5E2-2ayn%2Ban%5E2%2Bn\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ay%5E2-2ayn%2Ban%5E2%2Bn-x=0 ALIGN=MIDDLE  ALT=\"ay%5E2-2ayn%2Ban%5E2%2Bn-x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Maybe alternatively<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28y%5E2-2yn%2Bn%5E2%29=x-n ALIGN=MIDDLE  ALT=\"a%28y%5E2-2yn%2Bn%5E2%29=x-n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28x-n%29%2F%28y%5E2-2yn%2Bn%5E2%29 ALIGN=MIDDLE  ALT=\"a=%28x-n%29%2F%28y%5E2-2yn%2Bn%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because this gives a on one side and an expression in terms of n on the other side.<BR>\n" );
document.write( "Knowing that a and n are constants, any point on the parabola should give equal expressions for the member on<BR>\n" );
document.write( "the right-side.\r<BR>\n" );
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document.write( "Using the two given points, those points (6,-2) and (3,4),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%286-n%29%2F%28%28-2%29%5E2-2%28-2%29n%2Bn%5E2%29 ALIGN=MIDDLE  ALT=\"a=%286-n%29%2F%28%28-2%29%5E2-2%28-2%29n%2Bn%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%283-n%29%2F%284%5E2-2%2A4%2Bn%5E2%29 ALIGN=MIDDLE  ALT=\"a=%283-n%29%2F%284%5E2-2%2A4%2Bn%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The two expressions for a must be equal.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-n%29%2F%28%28-2%29%5E2-2%28-2%29n%2Bn%5E2%29=%283-n%29%2F%284%5E2-2%2A4%2Bn%5E2%29 ALIGN=MIDDLE  ALT=\"%286-n%29%2F%28%28-2%29%5E2-2%28-2%29n%2Bn%5E2%29=%283-n%29%2F%284%5E2-2%2A4%2Bn%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-n%29%2F%284%2B4n%2Bn%5E2%29=%283-n%29%2F%2816-8n%2Bn%5E2%29 ALIGN=MIDDLE  ALT=\"%286-n%29%2F%284%2B4n%2Bn%5E2%29=%283-n%29%2F%2816-8n%2Bn%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-n%29%2816-8n%2Bn%5E2%29=%283-n%29%284%2B4n%2Bn%5E2%29 ALIGN=MIDDLE  ALT=\"%286-n%29%2816-8n%2Bn%5E2%29=%283-n%29%284%2B4n%2Bn%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96-48n%2B6n%5E2-16n%2B8n%5E2-n%5E3=12%2B12n%2B3n%5E2-4n-4n%5E2-n%5E3 ALIGN=MIDDLE  ALT=\"96-48n%2B6n%5E2-16n%2B8n%5E2-n%5E3=12%2B12n%2B3n%5E2-4n-4n%5E2-n%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96-48n-16n%2B6n%5E2%2B8n%5E2=12%2B12n-4n%2B3n%5E2-4n%5E2 ALIGN=MIDDLE  ALT=\"96-48n-16n%2B6n%5E2%2B8n%5E2=12%2B12n-4n%2B3n%5E2-4n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96-64n%2B14n%5E2=12%2B8n-n%5E2 ALIGN=MIDDLE  ALT=\"96-64n%2B14n%5E2=12%2B8n-n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96-12-64n-8n%2B14n%5E2%2Bn%5E2=0 ALIGN=MIDDLE  ALT=\"96-12-64n-8n%2B14n%5E2%2Bn%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15n%5E2-72n%2B84=0 ALIGN=MIDDLE  ALT=\"15n%5E2-72n%2B84=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Divide this by 3;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%285n%5E2-24n%2B28=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%285n%5E2-24n%2B28=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "How is the discriminant?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%5E2-4%2A5%2A28 ALIGN=MIDDLE  ALT=\"24%5E2-4%2A5%2A28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576-20%2A28 ALIGN=MIDDLE  ALT=\"576-20%2A28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576-560 ALIGN=MIDDLE  ALT=\"576-560\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2816%29 ALIGN=MIDDLE  ALT=\"highlight_green%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a perfect square whole number.\r<BR>\n" );
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document.write( "Now, what can be n?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%2824%2B-+sqrt%2816%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"n=%2824%2B-+sqrt%2816%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%2824%2B-+4%29%2F10 ALIGN=MIDDLE  ALT=\"n=%2824%2B-+4%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=2%29 ALIGN=MIDDLE  ALT=\"highlight%28n=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=14%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28n=14%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "... Still not finished.  We want to use these values for n to get our value for a; probably a single (or maybe not) value.  You will have to try each of the solutions for n and find out.<BR>\n" );
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