Answer:
f(x + h) = -4x² - 4h² - 8hx + 3x + 3h
General Formulas and Concepts:
Algebra I
- Function Notation
- Expand by FOIL (First Outside Inside Last)
- Combining Like Terms
Step-by-step explanation:
Step 1: Define
f(x) = 3x - 4x²
f(x + h) is x = x + h
Step 2: Evaluate
- Substitute: f(x + h) = 3(x + h) - 4(x + h)²
- Expand [FOIL]: f(x + h) = 3(x + h) - 4(x² + 2hx + h²)
- Distribute: f(x + h) = 3x + 3h - 4x² - 8hx - 4h²
- Rewrite: f(x + h) = -4x² - 4h² - 8hx + 3x + 3h
