Question

How do you sketch the graph of `y=(x-3)^2` and describe the transformation?

Answer 1

The graph of `y` is the standard graph of `y=x^2` transformed 3 units positive on the `x-`axis.

Explanation:

`y=(x-3)^2`

Let `x'=x-3 -> x=x'+3`

Now, `y=(x')^2`

Hence, the graph of `y` is the standard graph of `y=x^2` transformed ("shifted") 3 units positive ("right") on the `x-`axis.

This can be seen by the graph of `y` below.

graph{(x-3)^2 [-3.146, 9.34, -1.97, 4.27]}