Transform f(x) = -x(x-8) to Its Standard Representation

To solve this problem, we'll convert the given function from its factored form to the standard form using the distributive property. The given function is $f(x) = -x(x - 8)$.

Let's go through the necessary steps:

• Step 1: Apply the distributive property to expand the expression.
  $f(x) = -x(x - 8) = -x \cdot x + (-x) \cdot (-8)$
• Step 2: Simplify each term.
  $-x \cdot x = -x^2$ and $(-x) \cdot (-8) = +8x$.
• Step 3: Combine the terms to express $f(x)$ in standard form:
  $f(x) = -x^2 + 8x$.

Therefore, the standard representation of the function is $f(x) = -x^2 + 8x$.

Comparing this result to the multiple-choice options, we can see that the correct choice is option 3: $f(x)=-x^2+8x$.