Answer:
f(x) = -2x² + 12x - 11
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) = -2(x - 3)² + 7
Step 2: Find Standard Form
- Expand by FOILing: f(x) = -2(x² - 6x + 9) + 7
- Distribute -2: f(x) = -2x² + 12x - 18 + 7
- Combine like terms (constants): f(x) = -2x² + 12x - 11
