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

Aug 9, 2017

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

#### Explanation:

$y = {\left(x - 3\right)}^{2}$

Let $x ' = x - 3 \to x = x ' + 3$

Now, $y = {\left(x '\right)}^{2}$

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]}