document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103838>Question 1103838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the range of f(x) = 3(x – 2)^2 + 3.\r<BR>\n" );
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document.write( "Is it all real numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718543 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=718543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No, parabolas always have a limited range. <BR>\n" );
document.write( "The domain is all real numbers. <BR>\n" );
document.write( "However the parabola is in vertex form which simplifies the solution. <BR>\n" );
document.write( "The quadratic coefficient, 3, is positive so the value at the vertex is the minimum.<BR>\n" );
document.write( "So the range would be [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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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