document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163001>Question 163001</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help.\r<BR>\n" );
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document.write( "Given the following information, find the range.\r<BR>\n" );
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document.write( "f(x)=2(x-3)^2 + 2\r<BR>\n" );
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document.write( "vertex is (3,2)\r<BR>\n" );
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document.write( "What is the range? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120205 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a quadratic equation of this kind (a parabola), the range is determined by the maximum or minimum and comes in the form of<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmx%5D ALIGN=MIDDLE  ALT=\"y%5Bmx%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "or<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bmn%5D ALIGN=MIDDLE  ALT=\"y%5Bmn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "The min or max occurs at the vertex.<BR>\n" );
document.write( "The only thing left to determine is whether f(3)=2 is a min or max value. <BR>\n" );
document.write( "That's determined by the coefficient (a) of 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;\" > term, <BR>\n" );
document.write( "if a>0, parabola opens up, min value.<BR>\n" );
document.write( "if a<0, parabola opens down, max value. <BR>\n" );
document.write( "In this case, a=2, min. value. <BR>\n" );
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document.write( "The range of the parabola is then,<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >) </SPAN>\n" );
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