Question 113828

In order to graph {{{y=(x+1)^3+4}}}, first graph its parent equation {{{y=x^3}}}

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



Now add 4 to the whole equation to shift the graph up 4 units  to get the new graph of {{{y=x^3+4}}} which looks like

{{{ graph(500, 500, -10, 10, -10, 10,x^3,x^3+4)}}} Graph of  {{{y=x^3}}}(red)  and  {{{y=x^3+4}}}(green)


Now replace x with x+1 to get {{{y=(x+1)^3+4}}} which shifts the graph to the left 1 unit 

So our new graph looks like



{{{ graph(500, 500, -10, 10, -10, 10,x^3,x^3+4,(x+1)^3+4)}}} Graph of  {{{y=x^3}}}(red), {{{y=x^3+4}}}(green), and  Graph of  {{{y=(x+1)^3+4}}}



So our final graph {{{y=(x+1)^3+4}}} alone looks like


{{{ graph(500, 500, -10, 10, -10, 10,(x+1)^3+4)}}}  Graph of  {{{y=(x+1)^3+4}}}