document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127806>Question 127806</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can I have some help finding a function whose graph is a parabola with vertex (6, -4) and that passes through the point (1, 8)?\r<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 #93611 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of a parabola with vertex at (h,k), and directrix at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=k-p ALIGN=MIDDLE  ALT=\"y=k-p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2=4p%28y-k%29 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2=4p%28y-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The vertex is given, so we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%5E2=4p%28y%2B4%29 ALIGN=MIDDLE  ALT=\"%28x-6%29%5E2=4p%28y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have to calculate p given that the parabola passes through (1,8).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-6%29%5E2=4p%288%2B4%29 ALIGN=MIDDLE  ALT=\"%281-6%29%5E2=4p%288%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=48p ALIGN=MIDDLE  ALT=\"25=48p\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=25%2F48 ALIGN=MIDDLE  ALT=\"p=25%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%5E2=4%2825%2F48%29%28y%2B4%29 ALIGN=MIDDLE  ALT=\"%28x-6%29%5E2=4%2825%2F48%29%28y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-12x%2B36=%2825%2F12%29%28y%2B4%29 ALIGN=MIDDLE  ALT=\"x%5E2-12x%2B36=%2825%2F12%29%28y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F25%29%28x%5E2-12x%2B36%29=y%2B4 ALIGN=MIDDLE  ALT=\"%2812%2F25%29%28x%5E2-12x%2B36%29=y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x%5E2-144x%2B432-100%29%2F25=y ALIGN=MIDDLE  ALT=\"%2812x%5E2-144x%2B432-100%29%2F25=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=y=%2812x%5E2-144x%2B332%29%2F25 ALIGN=MIDDLE  ALT=\"f%28x%29=y=%2812x%5E2-144x%2B332%29%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2C%0D%0Agraph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%2812x%5E2-144x%2B332%29%2F25%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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