1. **State the problem:** We are given the function $$f(x) = 3(x - 2)^2 - 7$$ and asked to write it in standard form. 2. **Recall the formula:** The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ where $a$, $b$, and $c$ are constants. 3. **Expand the squared term:** $$3(x - 2)^2 - 7 = 3(x^2 - 4x + 4) - 7$$ 4. **Distribute the 3:** $$= 3x^2 - 12x + 12 - 7$$ 5. **Combine like terms:** $$= 3x^2 - 12x + (12 - 7)$$ $$= 3x^2 - 12x + 5$$ 6. **Final answer:** $$f(x) = 3x^2 - 12x + 5$$ This is the standard form of the given quadratic function.