Question 87017
Start with the graph of {{{y=x^3}}}


{{{ graph( 500,500,-10,10,-10,10, x^3) }}}


Since we have {{{(x-2)^3}}} this means we shift the graph 2 units to the right.
So shift the graph 2 units to the right like this:


{{{ graph( 500,500,-10,10,-10,10, x^3, (x-2)^3) }}} Graph of {{{y=x^3}}} (red) and {{{y=(x-2)^3}}} (green)


Now since we're adding 2 to {{{y=(x-2)^3}}} to get {{{y=(x-2)^3+2}}} this means we shift the graph {{{y=(x-2)^3}}} up two units like this


{{{ graph( 500,500,-10,10,-10,10, x^3, (x-2)^3, (x-2)^3+2) }}} Graph of {{{y=x^3}}} (red) , {{{y=(x-2)^3}}} (green), and {{{y=(x-2)^3+2}}} (blue)


So the graph of {{{y=(x-2)^3+2}}} is 


{{{ graph( 500,500,-10,10,-10,10,(x-2)^3+2) }}} Graph {{{y=(x-2)^3+2}}}