document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=522226>Question 522226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would really appreciate you help.<BR>\n" );
document.write( "I have to write the equation in vertex form and tell whether it opens up or down.\r<BR>\n" );
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document.write( "1.  The vertex of the parabola is the (3,-2).  Point F (-2,-8) lies on the graph of the parabola.\r<BR>\n" );
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document.write( "Thank you so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #346747 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=346747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Since you are concerned with whether the parabola opens up or down I have to assume that the axis is a vertical line.  You don't say so, and there really is no other clue about the orientation of your parabola.  When you are writing descriptions of things, do not assume anything.  Had you stated that you wanted to derive a <i>function</i> whose graph was a parabola, that would have been a different thing.\r<BR>\n" );
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document.write( "The vertex form for a vertical axis parabola is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ a(x\ -\ h)^2\ +\ k\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(h,\,k\right)\"> are the coordinates of the vertex.\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ a(x\ -\ 3)^2\ -\ 2\">\r<BR>\n" );
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document.write( "Is true for this parabola, and if the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-2,\,-8\right)\"> is indeed on the graph, then the following must be true as well:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -8\ =\ a(-2\ -\ 3)^2\ -\ 2\">\r<BR>\n" );
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document.write( "Which is to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ -\frac{6}{25}\">\r<BR>\n" );
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document.write( "And the full vertex form equation becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -\frac{6}{25}(x\ -\ 3)^2\ -\ 2\">\r<BR>\n" );
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document.write( "Parabolas with a negative lead coefficient open downward.  This makes sense upon examining the two given points.  The vertex of any parabola function is either a minimum or a maximum.  Hence, if the value of the function (the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinate) at any point other than the vertex is less than the value of the function at the vertex, the vertex must be a maximum and that means the parabola must open downwards.  -8 is less than -2 QED.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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