document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=222527>Question 222527</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value\r<BR>\n" );
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document.write( "f(x) = 2xsquared + 2x - 6<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 #166617 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=166617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2x%5E2+%2B+2x+-+6+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+2x%5E2+%2B+2x+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "From the coefficient associated with the x^2 term, in this case, it's a POSITIVE TWO.  Since it is \"positive\" think \"smiley face\"-- so, it's a parabola that's opens upwards.  If it was \"negative\" think \"sad face\" -- so, it's a parabola that's opens downwards.<BR>\n" );
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document.write( "Since the coefficient is +2, it opens upwards thus the function will have a MINIMUM.<BR>\n" );
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document.write( "One way to find the vertex, is by completing the square.  Doing so you will get it into the \"vertex form\" of the equation:<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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2x%5E2+%2B+2x+-+6+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+2x%5E2+%2B+2x+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%28x%5E2+%2B+x+%2B+__%29++-+6+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%28x%5E2+%2B+x+%2B+__%29++-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%28x%5E2+%2B+x+%2B+1%2F4+%29++-+6+-+1%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%28x%5E2+%2B+x+%2B+1%2F4+%29++-+6+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%28x+%2B+1%2F2%29%5E2++-+13%2F2+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%28x+%2B+1%2F2%29%5E2++-+13%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%28x+-+%28-1%2F2%29%29%5E2++%2B+%28-13%2F2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%28x+-+%28-1%2F2%29%29%5E2++%2B+%28-13%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore, the vertex is at (-1/2, -13/2)<BR>\n" );
document.write( "or<BR>\n" );
document.write( "(-.5, -6.5)\r<BR>\n" );
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