Question

Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?

Answer 1

Answer:

f(x) shift right 2 and up 3 to get g(x)

A is correct.

Step-by-step explanation:

Given: $f(x)=x^2$ and $g(x)=(x-2)^2+3$

We need to find transformation that occurs from f(x) to g(x).

Parent function is quadratic equation.

Concept of transformation:-

For horizontal shift:

If x changes to x+a then left or right shift.

a>0 then shift left

a<0 then shift right

For vertical shift:

If y changes to y+a then up or down shift

If b>0 then shift up by a unit

If b<0 then shift down by a unit.

$f(x)\rightarrow g(x)$

$x^2\rightarrow(x-2)^2$

Thus, f(x) shift 2 unit right.

$(x-2)^2\rightarrow (x-2)^2+3$

Thus, f(x) shift 3 unit up.

Hence, f(x) shift right 2 and up 3 to get g(x)

Answer 2

Answer:

A. right 2, up 3

Step-by-step explanation:

We have that,

The function $f(x) = x^2$ is transformed to $g(x) =(x- 2)^2+3$.

We see that,

The function f(x) is translated 2 units to the right and 3 units upwards to obtain the function g(x).

So, the correct transformation is 'right 2, up 3'.

Hence, option A is correct.