document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446237>Question 446237</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the equation of a parabola y = (x-5)^2 + 4, I understand the vertex is (5,4). I don't understand why we take the opposite of what is in the parenthesis with the x.  It seems to me we would translate the vertex of the graph left 5 units, not right 5 units.  Can someone please help me understand this? Thanks. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307303 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=307303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the equation of a parabola y = (x-5)^2 + 4, I understand the vertex is (5,4). I don't understand why we take the opposite of what is in the parenthesis with the x. It seems to me we would translate the vertex of the graph left 5 units, not right 5 units.<BR>\n" );
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document.write( "Try thinking of it this way.<BR>\n" );
document.write( "If you had the equation y = x^2+4<BR>\n" );
document.write( "y would be 4 when x is zero.<BR>\n" );
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document.write( "You have the equation y = (x-5)^2 + 4<BR>\n" );
document.write( "y will be 4 when (x-5) is zero.<BR>\n" );
document.write( "That happens when x = 5.<BR>\n" );
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document.write( "What happened before at x = 0 now<BR>\n" );
document.write( "happens when x = 5.<BR>\n" );
document.write( "The graph has moved 5 to the right.<BR>\n" );
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document.write( "This is the way I teach the idea.<BR>\n" );
document.write( "Think of the x-axis as a time line where<BR>\n" );
document.write( "time flows from left to right i.e. 0 seconds, 1 second, ...., 5 seconds etc.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "t is some time on the t-axis.<BR>\n" );
document.write( "t-5 is 5 seconds later on the t-axis.<BR>\n" );
document.write( "\"later\" means to the right.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "t+5 would mean 5 seconds earlier.<BR>\n" );
document.write( "\"earlier\" means to the left.\r<BR>\n" );
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document.write( "Hope this helps.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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