Given `g(x)=4x^2 -8x+2` , what is the value of g(-5) ?

Options

A. 442
B. 142
C. 67
D. `-58`

Answer

To find the value of \( g(-5) \) for the function \( g(x) = 4x^2 - 8x + 2 \), we will follow these steps:

### Step 1: Substitute \(-5\) into the function
We start by substituting \(-5\) for \(x\) in the function \(g(x)\):
\[ g(-5) = 4(-5)^2 - 8(-5) + 2 \]

### Step 2: Calculate \((-5)^2\)
Next, we calculate \((-5)^2\):
\[ (-5)^2 = 25 \]
So, we can rewrite the equation:
\[ g(-5) = 4(25) - 8(-5) + 2 \]

### Step 3: Multiply \(4\) by \(25\)
Now, we multiply \(4\) by \(25\):
\[ 4(25) = 100 \]
Now our equation looks like:
\[ g(-5) = 100 - 8(-5) + 2 \]

### Step 4: Calculate \(-8(-5)\)
Next, we calculate \(-8(-5)\):
\[ -8(-5) = 40 \]
Now we can rewrite the equation:
\[ g(-5) = 100 + 40 + 2 \]

### Step 5: Add the numbers together
Finally, we add \(100\), \(40\), and \(2\):
\[ g(-5) = 100 + 40 + 2 = 142 \]

### Final Answer
Thus, the value of \( g(-5) \) is:
\[ \boxed{142} \]

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