Question

Consider the function f(x) = -2x2 +3x-8. Determine f(k+4). Fully simplify your answer.

Answer 1

f(k + 4) = -2k² - 13k - 28

General Formulas and Concepts:

Pre-Algebra

• Distributive Property

Algebra I

• Terms/Coefficients
• Expand by FOIL
• Functions
• Function Notation

Explanation:

Step 1: Define

Identify

f(x) = -2x² + 3x - 8

Step 2: Evaluate

1. Substitute in x [Function f(x)]: f(k + 4) = -2(k + 4)² + 3(k + 4) - 8
2. Expand [FOIL]: f(k + 4) = -2(k² + 8k + 16) + 3(k + 4) - 8
3. [Distributive Property] Distribute: f(k + 4) = -2k² - 16k - 32 + 3k + 12 - 8
4. Combine like terms: f(k + 4) = -2k² - 13k - 28