Question

Rewrite the function f(x)=-2(x-3)^2+7 in the form f(x)=ax^2+bx+c

Answer 1

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

Explanation:

Step 1: Define function

Vertex Form: f(x) = -2(x - 3)² + 7

Step 2: Find Standard Form

1. Expand by FOILing: f(x) = -2(x² - 6x + 9) + 7
2. Distribute -2: f(x) = -2x² + 12x - 18 + 7
3. Combine like terms (constants): f(x) = -2x² + 12x - 11