document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049030>Question 1049030</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.<BR>\n" );
document.write( "f(x) = 2x^2 - 2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664695 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=664695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Coefficient on the leading term is POSITIVE 2.  This parabola is concave upward, or convex downward; the  vertex is a minimum.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-2x=0 ALIGN=MIDDLE  ALT=\"2x%5E2-2x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28x-1%29=0 ALIGN=MIDDLE  ALT=\"2x%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-1%29=0 ALIGN=MIDDLE  ALT=\"x%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x-intercepts are at  0 and 1.  Because of symmetry the vertex (minimum point) will be at the exact middle of 0 and 1; or at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2F2%29=2%281%2F2%29%5E2-2%281%2F2%29 ALIGN=MIDDLE  ALT=\"f%281%2F2%29=2%281%2F2%29%5E2-2%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----compute this. </SPAN>\n" );
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