document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107754>Question 1107754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if x is a real number find the minimum value of 3^x^2-4x+8  (x to power of 2, x-4 not 2-4)\r<BR>\n" );
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document.write( "thanks for help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #722780 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=722780\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = 3x^2 - 4x + 8.\r<BR>\n" );
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document.write( "the min/max point on this quadratic equation is when x = -b/2a\r<BR>\n" );
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document.write( "the quadratic is in standard form of ax^2 + bx + c = 0 when y = 0.\r<BR>\n" );
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document.write( "therefore a = 3, b = -4, c = 8.\r<BR>\n" );
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document.write( "x = -b/2a becomes x = 4/6 = 2/3.\r<BR>\n" );
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document.write( "when x = 2/3, 3x^2 - 4x + 8 = 3 * 4/9 - 4 * 2/3 + 8 which is equal to 12/9 - 4 * 6/9 + 72/9 which is equal to 12/9 - 24/9 + 72/9 which is equal to 60/9.\r<BR>\n" );
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document.write( "since the coefficient of the x^2 term is positive, this equation will have a minimum value at (2/3, 60/9).\r<BR>\n" );
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document.write( "your minimum value for the equation is when x = 2/3 and y = 60/9.\r<BR>\n" );
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document.write( "in decimal form, that would be x = 0.667 and y = 6.667.\r<BR>\n" );
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document.write( "i graphed the equation of y = 3x^2 - 4x + 8 and the graph shows that the minimum point is at (.667,6.667), agreeing with the algebraic solution.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/012805.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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