Suppose the graph of `f(x)=2x^(2)` is translated 3 units down and 2 units right. If the resulting graph represents the graph of g(x), what is the value of `g(-1.2)` ?

Options

A. `-1.72`
B. `-0.12`
C. `2.88`
D. `17.48`

Explanation

To solve the problem step by step, we will follow the translation rules for the function \( f(x) = 2x^2 \).

### Step 1: Understand the translation
The function \( f(x) = 2x^2 \) is translated:
- 3 units down (which means we subtract 3 from the function)
- 2 units to the right (which means we replace \( x \) with \( x - 2 \))

### Step 2: Write the new function \( g(x) \)
Using the translation rules:
- For the right translation: \( x \) becomes \( x - 2 \)
- For the down translation: we subtract 3 from the function

Thus, we can express \( g(x) \) as:
\[ g(x) = f(x - 2) - 3 \]

### Step 3: Substitute \( f(x) \)
Now, substitute \( f(x) = 2x^2 \) into the equation:
\[ g(x) = 2(x - 2)^2 - 3 \]

### Step 4: Expand \( g(x) \)
Now we will expand \( g(x) \):
\[ g(x) = 2((x - 2)(x - 2)) - 3 \]
\[ = 2(x^2 - 4x + 4) - 3 \]
\[ = 2x^2 - 8x + 8 - 3 \]
\[ = 2x^2 - 8x + 5 \]

### Step 5: Calculate \( g(-1.2) \)
Now we need to find \( g(-1.2) \):
\[ g(-1.2) = 2(-1.2)^2 - 8(-1.2) + 5 \]

Calculating each term:
1. Calculate \( (-1.2)^2 \):
\[ (-1.2)^2 = 1.44 \]
2. Calculate \( 2(-1.2)^2 \):
\[ 2 \times 1.44 = 2.88 \]
3. Calculate \( -8(-1.2) \):
\[ -8 \times -1.2 = 9.6 \]
4. Combine all terms:
\[ g(-1.2) = 2.88 + 9.6 + 5 \]
\[ = 2.88 + 9.6 = 12.48 \]
\[ = 12.48 + 5 = 17.48 \]

### Final Answer
Thus, the value of \( g(-1.2) \) is:
\[ \boxed{17.48} \]