Question

Rewrite the function f(x)=3(x-1)^2+9 in the form f(x)=ax^2+bx+c

Answer 1

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

Explanation:

Step 1: Define function

Vertex Form: f(x) = 3(x - 1)² + 9

Step 2: Find Standard Form

1. Expand by FOILing: f(x) = 3(x² - 2x + 1) + 9
2. Distribute 3: f(x) = 3x² - 6x + 3 + 9
3. Combine like terms (constants): f(x) = 3x² - 6x + 12