`f(x)=(x-8)(x+2)` ,brgt Which of the following is an equivalent form of the function above in which the minimum value of function f appears in the equation as a constant?

Options

A. `f(x)=x^(2)-16`
B. `f(x)=(x+3)^(2)-16`
C. `f(x)=(x+3)^(2)-7`
D. `f(x)=(x-3)^(2)-25`

Answer

To find an equivalent form of the function \( f(x) = (x - 8)(x + 2) \) in which the minimum value of the function appears as a constant, we will follow these steps:

### Step 1: Expand the function
First, we will expand the function \( f(x) \).

\[ f(x) = (x - 8)(x + 2) \]
Using the distributive property (FOIL method):

\[ f(x) = x^2 + 2x - 8x - 16 \]
Combine like terms:

\[ f(x) = x^2 - 6x - 16 \]