document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204759>Question 1204759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How does the graph of g(x) = (x-4)² + 3 compare to the parent function f(x) = x²?<BR>\n" );
document.write( "A. g(x) is shifted 4 units to the left and 3 units up.<BR>\n" );
document.write( "B. g(x) is shifted 3 units to the right and 4 units down.<BR>\n" );
document.write( "C. g(x) is shifted 4 units to the right and 3 units up.<BR>\n" );
document.write( "D. g(x) is shifted 3 units to the left and 4 units up. </SPAN>\n" );
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document.write( "Answer: <font color=red size=4>Option C</font><BR>\n" );
document.write( "Shift 4 units right and 3 units up\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "When replacing x with x-4, we reduce the input by 4.<BR>\n" );
document.write( "This will move the xy axis 4 units to the left, and gives the illusion the parabola moves 4 units to the right (when holding the parabola fixed in place compared to the moving xy axis). <BR>\n" );
document.write( "I like to imagine the parabola etched in stone on a wall. <BR>\n" );
document.write( "The xy axis is allowed to move left/right, which can happen through a viewfinder of a camera perhaps.\r<BR>\n" );
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document.write( "In short, x-4 means \"shift 4 units right\". <BR>\n" );
document.write( "For students new to algebra, this may seem completely backwards. <BR>\n" );
document.write( "Some new students might incorrectly think the \"minus 4\" means \"shift left\" or \"shift in the negative x direction\". \r<BR>\n" );
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document.write( "The +3 at the end will move the curve up 3 units because each y coordinate is 3 units larger. <BR>\n" );
document.write( "A point like (5,1) moves to (5,4) as one example.\r<BR>\n" );
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document.write( "I recommend using a graphing tool like Desmos or GeoGebra to see how the transformations are taking place.<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.desmos.com/calculator/o42veth7sr\">https://www.desmos.com/calculator/o42veth7sr</a><BR>\n" );
document.write( "The order is red to blue to green<BR>\n" );
document.write( "y = x^2 in red<BR>\n" );
document.write( "y = (x-4)^2 in blue<BR>\n" );
document.write( "y = (x-4)^2 + 3 in green<BR>\n" );
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