document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866555>Question 866555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> vertically compress by a factor of 1/2 and translate down by 2<BR>\n" );
document.write( "y=x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522356 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=522356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We start with <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;\" >. That is given to us. This is the parent quadratic function/equation. This is the <font color=\"green\">green</font> graph shown below.\r<BR>\n" );
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document.write( "We would then \"vertically compress by a factor of 1/2\". So we would multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 1/2 which \"squishes\" the graph. This is because every point on the graph is now half as high as it used to be (ex: y = 4 ---> y = (1/2)*4 = 2 )\r<BR>\n" );
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document.write( "So we now have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+expr%281%2F2%29x%5E2 ALIGN=MIDDLE  ALT=\"y+=+expr%281%2F2%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is the <font color=\"blue\">blue</font> graph shown below.\r<BR>\n" );
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document.write( "Finally, we \"translate down by 2\" to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+expr%281%2F2%29x%5E2-2 ALIGN=MIDDLE  ALT=\"y+=+expr%281%2F2%29x%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Visually we are just shifting the entire blue graph 2 units down to get the <font color=\"purple\">purple</font> graph.\r<BR>\n" );
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document.write( "Below are the graphs of <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+expr%281%2F2%29x%5E2 ALIGN=MIDDLE  ALT=\"y+=+expr%281%2F2%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+expr%281%2F2%29x%5E2-2 ALIGN=MIDDLE  ALT=\"y+=+expr%281%2F2%29x%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <font color=\"green\">green</font>, <font color=\"blue\">blue</font> and <font color=\"purple\">purple</font> respectively.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A%0D%0A%0D%0A%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C0%2Cx%5E2%2C%281%2F2%29%2Ax%5E2%2C%281%2F2%29%2Ax%5E2-2%29%0D%0A%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The sequence of graphs above (all plotted on the same xy axis) shows us how <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;\" > transforms into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+expr%281%2F2%29x%5E2-2 ALIGN=MIDDLE  ALT=\"y+=+expr%281%2F2%29x%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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