Question

Which best describes the transformation that occurs from

the graph of f(x) = x² to g(x) = (x - 2)2 + 3?
right 2, up 3
left 2 down 3
right 2, down 3
left 2, up 3

Answer 1

right 2, up 3

Explanation:

The original function is:

`f(x) = x^2`

Translated to:

`g(x)=(x-2)^2+3`

Lets look at the constants that are added or subtracted to determine the transformation.

As -2 is is added to x (grouped with x), the transformation is a horizontal transformation. The shift is of two to the right.

As +3 is not grouped with x, the transformation is vertical. The shift is vertical shift of 3 to upward direction.

So the correct answer is:

right 2, up 3 ..