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 because when the change happens within x the opposite result happens but for vertical it remains the same . So the answer is right 2, up 3

Answer 2

we have

`f(x)=x^(2)`

This is a vertical parabola open upward

The vertex is the point
`(0,0)`

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

This is a vertical parabola open upward

The vertex is the point
`(2,3)`

The rule of the translation of f(x) to g(x) is

`(x,y)-----> (x+2,y+3)`

that means

the translation is
`2` units to the right and
`3` units up

therefore

the answer is the option

right 2, up 3