Question

Which transformations on the graph of f of x equals x squared will produce the graph of g of x equals left-parenthesis x minus 3 right-parenthesis squared minus 2?

Answer options with 4 options
A.
translate f of x left 3 units and up 2 units

B.
translate f of x left 3 units and down 2 units

C.
translate f of x right 3 units and up 2 units

D.
translate f of x right 3 units and down 2 units

Answer 1

To determine how the graph of \( f(x) = x^2 \) transforms into \( g(x) = (x - 3)^2 - 2 \), we can analyze the transformations step by step:

1. The term \( (x - 3)^2 \) indicates a horizontal translation:
- The expression \( (x - 3) \) means the graph is translated **right** by 3 units.

2. The term \( -2 \) indicates a vertical translation:
- The subtraction of 2 means the graph is translated **down** by 2 units.

Putting both transformations together, the graph of \( f(x) = x^2 \) is translated **right 3 units** and **down 2 units** to obtain the graph of \( g(x) = (x - 3)^2 - 2 \).

Thus, the correct answer is:

**D. translate f(x) right 3 units and down 2 units.**