document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102873>Question 102873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP TONIGHT if possible!  This problem doesn't come from a textbook, but it is the only one on the worksheet that I cannot solve.  Here it goes:\r<BR>\n" );
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document.write( "The graph of the square function (f(x) = x^2) has been transformed by rotating the graph about the x-axis, pushing the entire graph down 5 units, and then left 8 units.  <BR>\n" );
document.write( "Write the equation of the transformed graph.\r<BR>\n" );
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document.write( "Thanks so much!  If you can get it to me tonight, that would be great, since it is due by midnight!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74823 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=74823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You start with:<BR>\n" );
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document.write( "f(x) = x^2<BR>\n" );
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document.write( "You can rotate it about the x-axis by changing the sign of the function. Call the new function<BR>\n" );
document.write( "g(x). So for the first translation (about the x-axis), we have:<BR>\n" );
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document.write( "g(x) = -x^2<BR>\n" );
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document.write( "Next you want to shift the graph down by 5 units. Do this by just subtracting 5 from the<BR>\n" );
document.write( "function. So now we have two translations and the function is:<BR>\n" );
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document.write( "g(x) = -x^2 - 5<BR>\n" );
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document.write( "We have one more translation to do. To shift the graph to the left 8 units, replace x<BR>\n" );
document.write( "by x + 8. [Yep. The +8 shifts the graph to the left. If you had used -8, the graph would<BR>\n" );
document.write( "shift to the right.]  Anyhow, the resulting change to g(x) is:<BR>\n" );
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document.write( "g(x) = -(x + 8)^2 - 5<BR>\n" );
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document.write( "That's the answer. You might want to try plotting a few points of both functions just to <BR>\n" );
document.write( "satisfy yourself of the shifts. Here's a graph of the two. The red graph is f(x) and the<BR>\n" );
document.write( "green graph is g(x).<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-20%2C20%2C-20%2C20%2Cx%5E2%2C+-%28x+%2B+8%29%5E2+-5%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-20%2C20%2C-20%2C20%2Cx%5E2%2C+-%28x+%2B+8%29%5E2+-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you out and that you can understand how the answer comes about.<BR>\n" );
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