document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178103>Question 178103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which represents the range for -(y+3)=(x-4)^2 :<BR>\n" );
document.write( "a){y such that y is less than or equal to -3,y belongs to a set of real numbers}<BR>\n" );
document.write( "b){y such that y is greater than or equal to 4, y belongs to a set of real numbers}<BR>\n" );
document.write( "c){y such that y is less than or equal to 3, y belongs to a set of real numbers}<BR>\n" );
document.write( "d){y such that y is less than or equal to -4, y belongs to a set of real numbers}<BR>\n" );
document.write( "I hope someone canhelp me, I always have trouble with these:( </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133095 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=133095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i would say the answer would be (a).<BR>\n" );
document.write( "that would be:<BR>\n" );
document.write( "y <= -3<BR>\n" );
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document.write( "here's why<BR>\n" );
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document.write( "your original equation is:<BR>\n" );
document.write( "-(y+3) = (x-2)^2<BR>\n" );
document.write( "multiply both sides of this equation by (-1) to get:<BR>\n" );
document.write( "(y+3) = -(x-4)^2<BR>\n" );
document.write( "subtract 3 from both sides of this equation to get:<BR>\n" );
document.write( "y = -(x-4)^2 - 3<BR>\n" );
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document.write( "y has to be negative because - (x-4)^2 will always be less than or equal to 0 regardless of the value of x.<BR>\n" );
document.write( "if x is 4, (x-4)^2 = 0<BR>\n" );
document.write( "if x is less than 4, (x-4) is negative but when you square it you get a positive number and when you take - the positive number you get a negative number.<BR>\n" );
document.write( "if x is greater than 4, (x-4) is positive but when you square it, you still get a positive number and when you take - the positive number you get a negative number.<BR>\n" );
document.write( "since - (x-4)^2 can never be positive, the most it can be is 0.<BR>\n" );
document.write( "when it is 0, the value of y is -3.<BR>\n" );
document.write( "that means that y can never be greater than -3.<BR>\n" );
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document.write( "that means that (a) is the choice you want.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );