document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=273706>Question 273706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
document.write( "\n" );
document.write( "I'm having trouble with the following question...\r<BR>\n" );
document.write( "\n" );
document.write( "Find the x- and y- coordinates of the parabola vertex for the function<BR>\n" );
document.write( "f(x)=-3x^2+6x-1\r<BR>\n" );
document.write( "\n" );
document.write( "My textbook tells me to + and - the coefficient of x\r<BR>\n" );
document.write( "\n" );
document.write( "So I do this...<BR>\n" );
document.write( "f(x)=-3x^2+6x-1<BR>\n" );
document.write( "f(x)=-3x^2+6x+3-3-1<BR>\n" );
document.write( "f(x)=(-3x^2+6x+3)-3-1\r<BR>\n" );
document.write( "\n" );
document.write( "And now I need to factor and simplify\r<BR>\n" );
document.write( "\n" );
document.write( "any help appreciated.\r<BR>\n" );
document.write( "\n" );
document.write( "thank you, </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199917 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=199917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'm not sure what you are trying to say as to your textbook instructions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "However, here is how to find the vertex of a parabola when you have a quadratic function in standard form:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ ax^2\ +\ bx\ +\ c\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex is given by:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_v = \frac{-b}{2a}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and then the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinate of the vertex is given by:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y_v = f(x_v) = f\left(\frac{-b}{2a}\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So for your problem:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_v = \frac{-6}{2(-3)}\ =\ 1\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y_v = f(1) = -3(1)^2\ +\ 6(1)\ -\ 1\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can do your own arithmetic.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And look at a graph of your function to check your work:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28%0D%0A500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28%0D%0A500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A-3x%5E2%2B6x-1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );