document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356772>Question 356772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the vertex of the x and y coordinate, line of symmetry and maximum of f(x)<BR>\n" );
document.write( "f(x)=-2x^2+2x+7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254738 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=254738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the vertex of the x and y coordinate, line of symmetry and maximum of f(x)<BR>\n" );
document.write( "f(x)=-2x^2+2x+7\r<BR>\n" );
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document.write( "f(x) = -2x^2 + 2x + 7, this is of form f(x) = ax^2 + bx + c<BR>\n" );
document.write( "a = -2, a < 0, so parabola opens downwards\r<BR>\n" );
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document.write( "f(x) = -2x^2 + 2x + 7 is standard form of the parabolic equation<BR>\n" );
document.write( "converting to vertex form<BR>\n" );
document.write( "f(x) = -2(x^2 - x) + 7<BR>\n" );
document.write( "(-1/2)^2 = 1/4<BR>\n" );
document.write( "-2 * 1/4 = -2/4 = -1/2<BR>\n" );
document.write( "7 + 1/2 = 7 1/2 = 15/2<BR>\n" );
document.write( "the above 3 lines were completing the square to get below line<BR>\n" );
document.write( "f(x) = -2x^2 + 2x - 1/2 + 7 + 1/2 = -2(x^2 - x + 1/4) + 15/2<BR>\n" );
document.write( "f(x) = -2(x - 1/2)^2 + 15/2\r<BR>\n" );
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document.write( "this is now in vertex form of f(x) = a(x - h)^2 + k, where (h,k) is vertex\r<BR>\n" );
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document.write( "vertex is (1/2,15/2)\r<BR>\n" );
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document.write( "axis of symmetry -> x = h = 1/2\r<BR>\n" );
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document.write( "maximum of f(x) since parabola opens downwards is k or 15/2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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