Question

Rewrite the function f(x)=4(x-1)^2-2 in the form f(x)=ax^2+bx+c

Answer 1

f(x) = 4x² - 8x + 2

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

Explanation:

Step 1: Define function

Vertex Form: f(x) = 4(x - 1)² - 2

Step 2: Find Standard Form

1. Expand by FOILing: f(x) = 4(x² - 2x + 1) - 2
2. Distribute 4: f(x) = 4x² - 8x + 4 - 2
3. Combine like terms (constants): f(x) = 4x² - 8x + 2