document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762675>Question 762675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i graph this equation?\r<BR>\n" );
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document.write( "y=4/3x2+8/3x-8/3\r<BR>\n" );
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document.write( "Please give me the Vertex and 4 additional points, 2 on each side of the vertex so i can graph it.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464114 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=464114\">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( "The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">-coordinate of the vertex of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \psi(x)\ =\ ax^2\ +\ bx\ +\ c\"> is given by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_v\ =\ \frac{-b}{2a}\">\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">-coordinate of the vertex of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \psi(x)\ =\ ax^2\ +\ bx\ +\ c\">, namely <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y_v\">, is given by the value of the function at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_v\">, namely:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y_v\ =\ \psi(x_v)\ =\ a(x_v)^2\ +\ b(x_v)\ +\ c\">.\r<BR>\n" );
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document.write( "Now that you have the coordinates of the vertex, plot <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_v,\,y_v\right)\">.\r<BR>\n" );
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document.write( "As it turns out, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_v\"> is an integer in this problem, so pick another value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> that is 1 larger than <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_v\">.  Evaluate the function at this value:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \psi(x_v\,+\,1)\ =\ a(x_v\,+\,1)^2\ +\ b(x_v\,+\,1)\ +\ c\">.\r<BR>\n" );
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document.write( "Then plot <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_v\,+\,1,\,\psi(x_v\,+\,1)\right)\">.  Use the property of symmetry to determine that if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_v\,+\,1,\,\psi(x_v\,+\,1)\right)\"> is a point on your graph, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x_v\,-\,1,\,\psi(x_v\,+\,1)\right)\"> must also be on the graph. \r<BR>\n" );
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document.write( "Calculate  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_v\ +\ 2\"> and repeat the above process for your other two points, giving you 5 points in all including the vertex.\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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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