document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320535>Question 320535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem asks to find the vertex and graph the following quadratic function.<BR>\n" );
document.write( "y=-x+6x<BR>\n" );
document.write( " My professor says I need only turn in the coordinates. This is what I have tried... x=-b/2a = -6/2(-1) = -6/-2 =3  x=3\r<BR>\n" );
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document.write( "y=-2(3)^2+6(3)= -2(9) + 18 = -18 + 18=0  y=0  My book says the vertex is (3,9) so I am totally confused. I come up with (0,0) for the y intercept but I have no idea how that relates to me finding the coordinates for this graph. I have a very hard time grasping this concept.  Thanks for your time.\r<BR>\n" );
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document.write( "Tracy Jones </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229550 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=229550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "You did absolutely everything correctly except for one thing.\r<BR>\n" );
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document.write( "You began with the function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -x^2\ +\ 6x\">\r<BR>\n" );
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document.write( "You calculated the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{-b}{2a}\ =\ \frac{-6}{2(-1)}\ =\ 3\">\r<BR>\n" );
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document.write( "And then you proceeded to evaluate the function at this value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.  Here is where you made your error.\r<BR>\n" );
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document.write( "The function you started with was:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -x^2\ +\ 6x\">\r<BR>\n" );
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document.write( "But you evaluated:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -2x^2\ +\ 6x\ =\ -2(3)^2\ +\ 6(3)\ =\ 0\">\r<BR>\n" );
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document.write( "Your evaluation calculation is spot on, but where did you get that extra factor of 2 in the lead coefficient?\r<BR>\n" );
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document.write( "What you should have done:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -(3)^2\ +\ 6(3)\ =\ -9\ +\ 18\ =\ 9\">\r<BR>\n" );
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document.write( "and therefore the vertex is at the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (3,\,9)\">\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" );
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