Convert f(x) = (x-6)(x-2) to Its Standard Quadratic Form

To find the standard representation of the quadratic function $f(x) = (x - 6)(x - 2)$, follow these steps:

• Step 1: Apply the FOIL method to expand the expression.
  - First: Multiply the first terms: $x \times x = x^2$.
  - Outside: Multiply the outer terms: $x \times (-2) = -2x$.
  - Inside: Multiply the inner terms: $(-6) \times x = -6x$.
  - Last: Multiply the last terms: $(-6) \times (-2) = 12$.
• Step 2: Combine the results from the FOIL method.
  - Combine all the expanded terms: $x^2 - 2x - 6x + 12$.
• Step 3: Simplify by combining like terms.
  - Combine the $x$-terms: $-2x - 6x = -8x$.
  - The expanded and simplified form is: $f(x) = x^2 - 8x + 12$.

By expanding and simplifying the given product, we have converted it to its standard form. Therefore, the standard representation of the function is $f(x) = x^2 - 8x + 12$.

The correct choice from the provided options is choice 2: $f(x) = x^2 - 8x + 12$.