document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047075>Question 1047075</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve this equation<BR>\n" );
document.write( "Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = 2x2 - 2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662543 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=662543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 2x2 - 2x\r<BR>\n" );
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document.write( "You mean to say,  f(x) = 2x^2 - 2x\r<BR>\n" );
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document.write( "which will become rendered as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E2-2x ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E2-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Is the coefficient on the leading term positive, or is it negative?  Vertex minimum if this coefficient is positive.\r<BR>\n" );
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document.write( "So you have your answer.<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=highlight_green%282%29x%5E2-2x ALIGN=MIDDLE  ALT=\"f%28x%29=highlight_green%282%29x%5E2-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------you know the lead coefficient is positive.  The reference model parabola equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2=1%2Ax%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2=1%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and you already know what this looks like graphed:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-6%2C6%2C-6%2C6%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and what if the lead coefficient were 2 instead of 1, still positive?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-6%2C6%2C-6%2C6%2C2x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-6%2C6%2C-6%2C6%2C2x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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