Here we have a problem with translations.
We will find that the correct option is C: g(x) = x^2-6x+14
We can define:
Horizontal translation:
For a general function f(x) an horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the shift is to the left
If N is negative, the shift is to the right.
Vertical translation:
For a general function f(x) a vertical translation of N units is written as:
g(x) = f(x) + N
If N is positive, the shift is upwards
If N is negative, the shift is downwards.
Here we know that:
Function g(x) is a transformation of f(x) = x^2
First, we apply a translation to the right of 3 units, then at the moment we have:
g(x) = f(x - 3)
Then we translate the graph down 5 units, then:
g(x) = f(x - 3) - 5
Now we can replace it by the actual function to get:
g(x) = (x - 3)^2 - 5
= x^2 - 2*3*x + 9 - 5
= x^2 - 6x + 4
Then the function is:
g(x) = x^2 - 6x + 4
Thus the correct option is C.
If you want to learn more, you can read:
https://brainly.com/question/5027860
