Why do you think we do the opposite motion when the function translates along the x axis? [br][br]Hint: Look at [math]\left(x-h\right)^2[/math]. Notice that when the graph moves along the positive x direction the function looks like (x - h) but when the function moves in the negative x direction the function looks like (x + h). Why do you think this happens?
[b]We do the “opposite” motion because horizontal shifts change the [i]input[/i] of the function.[/b][br]In [i]f(x−h)[/i], the function subtracts [i]h[/i], so we must move the graph [b]right[/b] to compensate.[br]In [i]f(x+h)[/i], it adds [i]h[/i], so we move the graph [b]left[/b].