document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724219>Question 724219</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Take the graph of y=2^x and transform it into y= -3(2)^(2x-4). Label 3 key points on both graphs.\r<BR>\n" );
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document.write( "I've tried graphing it and applying the required stretches and transformations (vertical stretch by 3, horizontal stretch by 1/2, reflection on x-axis, horizontal translation 4 units left) but my graph doesn't match the graph I plug into the calculator. Am I doing something wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443691 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming you meant y equals x squared (y=x^2):<BR>\n" );
document.write( "To transform <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%282x-4%29%5E2 ALIGN=MIDDLE  ALT=\"y=-3%282x-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "you need a horizontal translation by 2 units right,<BR>\n" );
document.write( "because you replaced <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x-2 ALIGN=MIDDLE  ALT=\"z=x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z=2%28x-2%29=2x-4 ALIGN=MIDDLE  ALT=\"2z=2%28x-2%29=2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A little algebra to get a simplified formula for the same function could have helped:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%282x-4%29%5E2 ALIGN=MIDDLE  ALT=\"y=-3%282x-4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%282%28x-2%29%29%5E2 ALIGN=MIDDLE  ALT=\"y=-3%282%28x-2%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%282%5E2%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"y=-3%282%5E2%28x-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%284%28x-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"y=-3%284%28x-2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-12%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"y=-12%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you would need a vertical stretch by 12, reflection on x-axis, and horizontal translation 2 units right.<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE: If you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3sqrt%282x-4%29 ALIGN=MIDDLE  ALT=\"y=-3sqrt%282x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the same thing applies.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%28x%29=%28x-2%29 ALIGN=MIDDLE  ALT=\"z%28x%29=%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > puts <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > 2 units to the left by subtracting 4, but<BR>\n" );
document.write( "in the compound function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to get the same y value you need to add 4 to x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28z%2B2%29=f%28x-2%2B2%29=f%28%28x%2B2%29-2%29=f%28x%29=y ALIGN=MIDDLE  ALT=\"f%28z%2B2%29=f%28x-2%2B2%29=f%28%28x%2B2%29-2%29=f%28x%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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