Answer:
f(x) = 3x² - 6x + 12
General Formulas and Concepts:
- Order of Operations: BPEMDAS
- Expand by FOIL (First Outside Inside Last)
- Standard Form: f(x) = ax² + bx + c
- Vertex Form: f(x) = a(bx + c)² + d
Step-by-step explanation:
Step 1: Define function
Vertex Form: f(x) = 3(x - 1)² + 9
Step 2: Find Standard Form
- Expand by FOILing: f(x) = 3(x² - 2x + 1) + 9
- Distribute 3: f(x) = 3x² - 6x + 3 + 9
- Combine like terms (constants): f(x) = 3x² - 6x + 12
