document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204394>Question 1204394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find g(x), where g(x) is the translation 3 units left of f(x)=x2.<BR>\n" );
document.write( "Write your answer in the form a(x  -  h)2+k, where a, h, and k are integers.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840598 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer:  <font color=red>g(x) = (x+3)^2</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation:<BR>\n" );
document.write( "Imagine that the parabola is stuck in place. What's allowed to move is only the xy axis. If we moved the xy axis 3 units to the right, then it gives the illusion the parabola moves 3 units to the left.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To move the xy axis 3 units to the right, we replace each old input x with the new input x+3.<BR>\n" );
document.write( "This will mean x^2 updates to (x+3)^2 as the answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A point like the vertex (0,0) on f(x) moves 3 units to the left to arrive at (-3,0) on g(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-6%2C4%2C-5%2C5%2C-1000%2Cx%5E2%2C%28x%2B3%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-6%2C4%2C-5%2C5%2C-1000%2Cx%5E2%2C%28x%2B3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f(x) = x^2 in green<BR>\n" );
document.write( "g(x) = (x+3)^2 in blue\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "GeoGebra and Desmos are two graphing tools I recommend.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );