To obtain the graph of  `y=(x -color(red)(2))^3+color(blue)(3)`, first sketch the function `y=x^3`.

Sketch the function `y=x^3`.  Remember the formula `y=(x-h)^3 +c` when applied to `y=x^3` (can be rewritten as `y=(x-color(red)(0))^3+color(blue)(0)`) has its inflection point at `(color(red)(0),color(blue)(0))`.

Using the formula `y=(x-h)^3 +c` for horizontal and vertical translations (shifts) and remembering that the point `(h,c)` is the inflection point of the function, the inflection point for `y=(x -color(red)(2))^3+color(blue)(3)` is `(color(red)(2),color(blue)(3))`.

Sketch the curve for `y=(x -color(red)(2))^3+color(blue)(3)` through its inflection point `(color(red)(2),color(blue)(3))` following the same shape as `y=x^3`.

To obtain the graph of  `y=x^2 – 6x + 11`, first sketch the function `y=x^2`.

Sketch the function `y=x^2`.  Remember the formula `y=(x-color(red)(h))^2 +color(blue)(c)` when applied to `y=x^2` (can be rewritten as `y=(x-color(red)(0))^2+color(blue)(0)`) has its vertex at `(color(red)(0),color(blue)(0))`.

Then rewrite `y=x^2 – 6x + 11` in the standard form by completing the square.

`y=(x^2-6x+9)-9+11`

`y=(x -3)^2+2`.

Remember the standard form is `y=(x-h)^2 +c`.

Using the formula `y=(x-h)^2 +c` for horizontal and vertical translations (shifts) and remembering that the point `(h,c)` is the vertex of the function, the vertex point for `y=(x -color(red)(3))^2+color(blue)(2)` is `(color(red)(3),color(blue)(2))`.

Sketch the curve for `y=(x -color(red)(3))^2+color(blue)(2)` through its vertex point `(color(red)(3),color(blue)(2))` following the same shape as `y=x^2`.