Question

If r(x)=4x^2-3x+7, Find r(2a^2)

Answer 1

r(2a²) = 16a⁴ - 6a² + 7

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

• Functions
• Function Notation
• Exponential Rule [Powering]:
  `\displaystyle (b^m)^n = b^(m \cdot n)`

Explanation:

Step 1: Define

Identify

r(x) = 4x² - 3x + 7

Step 2: Evaluate

1. Substitute in x [Function r(x)]: r(2a²) = 4(2a²)² - 3(2a²) + 7
2. Exponential Rule [Powering]: r(2a²) = 4(2²a²⁽²⁾) - 3(2a²) + 7
3. [Exponents] Multiply: r(2a²) = 4(2²a⁴) - 3(2a²) + 7
4. Exponents: r(2a²) = 4(4a⁴) - 3(2a²) + 7
5. Multiply: r(2a²) = 16a⁴ - 6a² + 7