document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162833>Question 162833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve the following:\r<BR>\n" );
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document.write( "For the graph of the function f(x)=2x^2-12x+20\r<BR>\n" );
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document.write( "Find the vertex; state whether this is a maximum or minimum value and find the value; and find the range.\r<BR>\n" );
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document.write( "I have no idea where to begin to solve this. Any assistance you can provide is greatly appreciated!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120017 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This site gives some insight into parabolas:<BR>\n" );
document.write( "http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php<BR>\n" );
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document.write( "Standard vertex form is:<BR>\n" );
document.write( "y= a(x-h)^2+k <BR>\n" );
document.write( "where<BR>\n" );
document.write( "(h,k) is the vertex<BR>\n" );
document.write( "Minimum or maximum is determined by the 'a'.<BR>\n" );
document.write( "If a is POSITIVE (think happy face -- smile -- U) -- opens upwards -- will be a minimum.<BR>\n" );
document.write( "If a is NEGATIVE (think sad face -- upside down U) -- opens downwards -- will be a maximum.<BR>\n" );
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document.write( "Idea is to get your equation into that form.<BR>\n" );
document.write( "f(x)=2x^2-12x+20<BR>\n" );
document.write( "Group terms:<BR>\n" );
document.write( "f(x)=(2x^2-12x)+20<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "f(x)=2(x^2-6x)+20<BR>\n" );
document.write( "Complete the square:<BR>\n" );
document.write( "f(x)=2(x^2-6x+9)+20-18<BR>\n" );
document.write( "f(x)=2(x-3)^2+2<BR>\n" );
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document.write( "Vertex is then (3,2)<BR>\n" );
document.write( "Since 'a' is POSITIVE, it is a MINIMUM.\r<BR>\n" );
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