Question

Explain how they got the answer. Calculus I

Answer 1

See explanation.

General Formulas and Concepts:

Pre-Algebra

• Distributive Property

Algebra I

• Terms/Coefficients
• Expanding

Explanation:

Step 1: Define

Identify

f(x - 3) = -(x - 3)² + 6(x - 3) - 11

Step 2: Simplify

1. Expand: f(x - 3) = -(x² - 6x + 9) + 6(x - 3) - 11
2. [Distributive Property] Distribute 6: f(x - 3) = -(x² - 6x + 9) + 6x - 18 - 11
3. [Distributive Property] Distribute negative: f(x - 3) = -x² + 6x - 9 + 6x - 18 - 11
4. Combine like terms: f(x - 3) = -x² + 12x - 38