What is the value of 3x squared when x = 2?
The Correct Answer and Explanation is :
To find the value of (3x^2) when (x = 2), we start by substituting the value of (x) into the expression.
Calculation:
- Substitute (x) with (2):
[
3x^2 = 3(2)^2
] - Calculate (2^2):
[
2^2 = 4
] - Now substitute (4) back into the expression:
[
3(4) = 12
]
Thus, the value of (3x^2) when (x = 2) is 12.
Explanation:
The expression (3x^2) represents a quadratic function, where the variable (x) is squared and then multiplied by the coefficient (3). Quadratic functions have important applications in various fields, including physics, engineering, and economics, as they can describe parabolic trajectories, optimization problems, and more.
Step-by-step Explanation:
- Understanding the Expression: The expression (3x^2) consists of three parts: the coefficient (3), the variable (x), and the exponent (2). The exponent signifies that the variable (x) is multiplied by itself.
- Substituting the Value: When we substitute (x = 2), we are finding the specific value of the expression for this given (x). This is a crucial step in evaluating expressions and is often done in algebraic calculations.
- Performing the Squaring Operation: Squaring a number means multiplying it by itself. Therefore, (2^2) yields (4). This part of the calculation emphasizes the importance of order of operations in mathematics, ensuring we handle exponents before multiplication.
- Final Multiplication: Multiplying (4) by (3) gives (12). This shows how coefficients in algebra can scale the value of expressions significantly.
Overall, this simple calculation illustrates the basic principles of algebra, highlighting the importance of understanding expressions, operations, and their properties in solving mathematical problems.