document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206777>Question 1206777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the range of y = -x^2 - 2x + 3<BR>\n" );
document.write( "A. x ≤ 4<BR>\n" );
document.write( "B. x ≤ -4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844413 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "One can only guess what the purpose of this problem is...<br><BR>\n" );
document.write( "Exactly as shown, the problem makes no sense, because the range of a function is the set of y values it takes on; the two answer choices are both in terms of x.<br><BR>\n" );
document.write( "If we guess that in fact the two answer choices were supposed to be in terms of y, then we only need to find the y coordinate of the vertex.<br><BR>\n" );
document.write( "The x coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29=2%2F-2=-1 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29=2%2F-2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >; the y value at the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28-1%29%5E2-2%28-1%29%2B3=-1%2B2%2B3=4 ALIGN=MIDDLE  ALT=\"-%28-1%29%5E2-2%28-1%29%2B3=-1%2B2%2B3=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER (I guess...?): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=4 ALIGN=MIDDLE  ALT=\"y%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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