Question

Evaluate f(x+3) when f(x)=-x^2-2x+2

Answer 1

f(x + 3) = -x² - 8x - 13

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Function Notation
• Expanding
• Terms/Coefficients/Degrees

Explanation:

Step 1: Define

f(x) = -x² - 2x + 2

f(x + 3) is x = x + 3

Step 2: Find

1. Substitute in x: f(x + 3) = -(x + 3)² - 2(x + 3) + 2
2. Expand: f(x + 3) = -(x² + 6x + 9) - 2x - 6 + 2
3. Distribute -1: f(x + 3) = -x² - 6x - 9 - 2x - 6 + 2
4. Combine like terms: f(x + 3) = -x² - 8x - 13