document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165141>Question 1165141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://answers.yahoo.com/question/index?qid=20200917201613AAEazzn\r<BR>\n" );
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document.write( "Help with this problem  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789599 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are two transformations to get from <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;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B2%29%5E2-3 ALIGN=MIDDLE  ALT=\"y=%28x%2B2%29%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "To determine the order of the transformations, consider how you would evaluate the new function for a given x value: add 2, square it, then subtract 3.<br><BR>\n" );
document.write( "So the adding 2 is the first transformation, and the subtracting 3 is the second.<br><BR>\n" );
document.write( "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;\" > has it minimum value when x=0; that value is 0.  So the vertex of the graph is at (0,0).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-4%2C4%2C-4%2C20%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-4%2C4%2C-4%2C20%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The first transformation is from <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;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That transformation moves the whole graph 2 units to the LEFT.<br><BR>\n" );
document.write( "Moving the graph LEFT when the transformed equation is x PLUS 2 squared is confusing to many beginning students.  But it makes perfect sense if you look at it this way:<br><BR>\n" );
document.write( "The graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"y+=+%28x%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has its minimum value when x+2=0 -- but that is when x = -2.<br><BR>\n" );
document.write( "So now the vertex is at (-2,0).<br><BR>\n" );
document.write( "So the first transformation moves the whole graph 2 units to the left:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-4%2C4%2C-4%2C20%2Cx%5E2%2C%28x%2B2%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-4%2C4%2C-4%2C20%2Cx%5E2%2C%28x%2B2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The second transformation is from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2-3 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  It should be easy to understand that this transformation simply moves the whole graph down 3 units; so now the vertex is at (-2,-3):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-4%2C4%2C-4%2C20%2Cx%5E2%2C%28x%2B2%29%5E2%2C%28x%2B2%29%5E2-3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-4%2C4%2C-4%2C20%2Cx%5E2%2C%28x%2B2%29%5E2%2C%28x%2B2%29%5E2-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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