If `f (x ) = 2x ^(2) + 7x -3,` what is the value of `g (-2)` ?

Options

A. `-25`
B. `-9`
C. `-1`
D. `3`

Explanation

To find the value of \( f(-2) \) for the function \( f(x) = 2x^2 + 7x - 3 \), we will follow these steps:

### Step 1: Substitute \(-2\) for \(x\) in the function
We need to find \( f(-2) \), so we will replace \( x \) in the function with \(-2\).

\[ f(-2) = 2(-2)^2 + 7(-2) - 3 \]

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

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

### Step 3: Multiply by 2
Now, we multiply this result by 2:

\[ 2 \times 4 = 8 \]

### Step 4: Calculate \(7 \times (-2)\)
Next, we calculate \(7 \times (-2)\):

\[ 7 \times (-2) = -14 \]

### Step 5: Combine all parts
Now we combine all the parts we have calculated:

\[ f(-2) = 8 - 14 - 3 \]

### Step 6: Simplify the expression
Now, we simplify the expression:

\[ 8 - 14 = -6 \]
\[ -6 - 3 = -9 \]

### Final Result
Thus, the value of \( f(-2) \) is:

\[ f(-2) = -9 \]

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