document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465221>Question 465221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following quadratic equation, determine if it has a maximum or a minimum value. Then find the maximum or minimum value. Please show all of your work.<BR>\n" );
document.write( "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 #318776 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318776\">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%2B2x ALIGN=MIDDLE  ALT=\"f%28x%29+=+-2x%5E2%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember that when the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the parabola equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=negative ALIGN=MIDDLE  ALT=\"negative\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the parabola opens <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=downwards ALIGN=MIDDLE  ALT=\"downwards\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore, it has a maximum value.\r<BR>\n" );
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document.write( "ANSWER: The quadratic function has a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MAXIMUM ALIGN=MIDDLE  ALT=\"MAXIMUM\"   DISABLED_style= \"max-width:90%; height:auto;\" > value.\r<BR>\n" );
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document.write( "Remember that the vertex of a parabola occurs at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "Given: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-2x%5E2%2B2x ALIGN=MIDDLE  ALT=\"f%28x%29+=+-2x%5E2%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Means: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-2 ALIGN=MIDDLE  ALT=\"a+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+2 ALIGN=MIDDLE  ALT=\"b+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=0 ALIGN=MIDDLE  ALT=\"c=0\"   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=h+=+-b+%2F+2a ALIGN=MIDDLE  ALT=\"h+=+-b+%2F+2a\"   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=h+=+-2+%2F+2%28-2%29 ALIGN=MIDDLE  ALT=\"h+=+-2+%2F+2%28-2%29\"   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=h+=+-2+%2F+-4 ALIGN=MIDDLE  ALT=\"h+=+-2+%2F+-4\"   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=h+=+1+%2F2 ALIGN=MIDDLE  ALT=\"h+=+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=k+=+%28-b-4ac%29+%2F+4a ALIGN=MIDDLE  ALT=\"k+=+%28-b-4ac%29+%2F+4a\"   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=k+=+%28-2-4%28-2%29%2A0%29+%2F+4%28-2%29 ALIGN=MIDDLE  ALT=\"k+=+%28-2-4%28-2%29%2A0%29+%2F+4%28-2%29\"   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=k+=+-2+%2F-8 ALIGN=MIDDLE  ALT=\"k+=+-2+%2F-8\"   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=k+=+1%2F4 ALIGN=MIDDLE  ALT=\"k+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the vertex: is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F2 ALIGN=MIDDLE  ALT=\"1+%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2F4 ALIGN=MIDDLE  ALT=\"1+%2F4\"   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=+graph%28+500%2C+500%2C+-5%2C+5%2C+-10%2C+5%2C+-2x%5E2%2B2x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-5%2C+5%2C+-10%2C+5%2C+-2x%5E2%2B2x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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