Question

Rewrite the function f(x)=-2(x+2)^2+6 in the form f(x)=ax^2+bx+c

Answer 1

f(x) = -2x² - 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) = -2(x + 2)² + 6

Step 2: Find Standard Form

1. Expand by FOILing: f(x) = -2(x² + 4x + 4) + 6
2. Distribute -2: f(x) = -2x² - 8x - 8 + 6
3. Combine like terms (constants): f(x) = -2x² - 8x - 2