Expand and Simplify: Transforming f(x) = 3x(x+4) to Standard Form

To find the standard representation of the quadratic function $f(x) = 3x(x + 4)$, follow these steps:

• Step 1: Apply the distributive property to expand the expression $x(x + 4)$.
  Using this property, we have:
  $x(x + 4) = x \cdot x + x \cdot 4 = x^2 + 4x$.
• Step 2: Multiply each term by the coefficient outside the parenthesis, which is 3.
  This gives us:
  $3(x^2 + 4x) = 3 \cdot x^2 + 3 \cdot 4x$.
• Step 3: Simplify by performing the multiplication.
  $3x^2 + 12x$.

Therefore, the standard representation of the function is $f(x) = 3x^2 + 12x$. This matches choice 3 in the provided answers.