Transforming Quadratics: Find the Standard Form of f(x) = (x-3)² + x

To solve this problem, we'll perform these steps:

• Expand $(x-3)^2$ using the formula for a square:
  $(x-3)^2 = x^2 - 2 \times x \times 3 + 3^2 = x^2 - 6x + 9$
• Add the $x$ from $f(x) = (x-3)^2 + x$ to the expanded terms:
  $x^2 - 6x + 9 + x$
• Combine like terms:
  $x^2 - 6x + x + 9 = x^2 - 5x + 9$

Therefore, the standard form of the function $f(x)$ is $f(x) = x^2 - 5x + 9$.

Thus, the correct choice is Choice 3.