document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23682>Question 23682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how would you graph the following fuctions?\r<BR>\n" );
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document.write( "1) y=1/2(x-3)2 +1\r<BR>\n" );
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document.write( "and y=-(x+4)2 -5 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12492 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12492\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You probably already know that the graph 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;\" > looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C+-10%2C+10%2C-10%2C+10%2C+x%5E2+%29 ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C+-10%2C+10%2C-10%2C+10%2C+x%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Well, these graphs will be similar, but because of the (x-3) you will be moving the graph of y =x^2 to the RIGHT 3 units. Because of the +1 added to the end of the equation, the graph will be moved UP 1 unit.  And because of the 1/2 coefficient, it opens up the graph and makes it wider.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28400%2C400%2C+-10%2C10%2C-10%2C10%2C+%281%2F2%29%2A%28x-3%29%5E2+%2B1%29+ ALIGN=MIDDLE  ALT=\"graph+%28400%2C400%2C+-10%2C10%2C-10%2C10%2C+%281%2F2%29%2A%28x-3%29%5E2+%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For your second graph, it says <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28x%2B4%29%5E2+-5 ALIGN=MIDDLE  ALT=\"y=-%28x%2B4%29%5E2+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the (x+4) moves the graph to the LEFT 4, the -5 at the end of the equation moves the graph DOWN 5 units, and the negative coefficient in front of the squared term INVERTS the graph! It should look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28400%2C400%2C+-10%2C10%2C-10%2C10%2C-%28x%2B4%29%5E2+-5%29 ALIGN=MIDDLE  ALT=\"graph+%28400%2C400%2C+-10%2C10%2C-10%2C10%2C-%28x%2B4%29%5E2+-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R^2 at SCC \r<BR>\n" );
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