If `f(x)=3x^(2)-2x+4,f(-2)=`

Options

A. `-12`
B. `-4`
C. `-2`
D. 20

Explanation

To find the value of \( f(-2) \) for the function \( f(x) = 3x^2 - 2x + 4 \), we will follow these steps:

### Step 1: Substitute \( x = -2 \) into the function
We start by substituting \(-2\) for \(x\) in the function \(f(x)\).

\[ f(-2) = 3(-2)^2 - 2(-2) + 4 \]

### Step 2: Calculate \((-2)^2\)
Next, we calculate \((-2)^2\):

\[ (-2)^2 = 4 \]

### Step 3: Multiply by 3
Now, we multiply the result by 3:

\[ 3 \times 4 = 12 \]

### Step 4: Calculate \(-2 \times -2\)
Now, we calculate \(-2 \times -2\):

\[ -2 \times -2 = 4 \]

### Step 5: Combine all parts
Now we can combine all the parts together:

\[ f(-2) = 12 + 4 + 4 \]

### Step 6: Add the values
Finally, we add these values together:

\[ 12 + 4 + 4 = 20 \]

Thus, the value of \( f(-2) \) is

\[ \boxed{20} \]

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