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

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Answer 1 · 2017-08-09T02:55:22

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

$y=(x-3)^2$

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]}

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