document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115511>Question 115511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the graph of  is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84056 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=84056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "Remember, if an equation is in vertex form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then we know the vertex is (h,k)\r<BR>\n" );
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document.write( "Since we can see that the vertex is (-6,0), this means h=-6 and k=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the general equation in vertex form. In this case, a=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-%28-6%29%29%5E2%2B0 ALIGN=MIDDLE  ALT=\"y=%28x-%28-6%29%29%5E2%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in h=-6 and k=0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B6%29%5E2%2B0 ALIGN=MIDDLE  ALT=\"y=%28x%2B6%29%5E2%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%28-6%29 ALIGN=MIDDLE  ALT=\"x-%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6 ALIGN=MIDDLE  ALT=\"x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B6%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x%2B6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Remove the zero term.\r<BR>\n" );
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document.write( "So the equation of the parabola that has been shifted 6 units to the left is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B6%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x%2B6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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