Evaluate $3x^2 - 1$ When $x = 2$.A. 3 B. 35 C. 11 D. 5

Introduction

In algebra, evaluating quadratic expressions is a crucial skill that helps us find the value of an expression when a variable is replaced by a specific value. In this article, we will focus on evaluating the quadratic expression $3x^2 - 1$ when $x = 2$. We will break down the process into simple steps and provide a clear explanation of each step.

What is a Quadratic Expression?

A quadratic expression is a polynomial expression of degree two, which means it has a variable raised to the power of two. It is typically written in the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. In our case, the quadratic expression is $3x^2 - 1$, where $a = 3$, $b = 0$, and $c = -1$.

Evaluating the Quadratic Expression

To evaluate the quadratic expression $3x^2 - 1$ when $x = 2$, we need to substitute $x = 2$ into the expression and simplify. Here are the steps:

Step 1: Substitute x = 2 into the Expression

We will replace $x$ with $2$ in the expression $3x^2 - 1$. This gives us:

$$3(2)^2 - 1$$

Step 2: Simplify the Expression

Now, we will simplify the expression by evaluating the exponent and multiplying the numbers. We have:

$$3(2)^2 - 1 = 3(4) - 1 = 12 - 1 = 11$$

Conclusion

In this article, we evaluated the quadratic expression $3x^2 - 1$ when $x = 2$. We broke down the process into simple steps and provided a clear explanation of each step. By following these steps, we were able to find the value of the expression, which is $11$. This demonstrates the importance of evaluating quadratic expressions in algebra.

Why is Evaluating Quadratic Expressions Important?

Evaluating quadratic expressions is an essential skill in algebra because it helps us find the value of an expression when a variable is replaced by a specific value. This is useful in a variety of situations, such as:

• Solving equations: Evaluating quadratic expressions is a crucial step in solving equations that involve quadratic expressions.
• Graphing functions: Evaluating quadratic expressions helps us graph functions and understand their behavior.
• Real-world applications: Quadratic expressions are used in many real-world applications, such as physics, engineering, and economics.

Common Mistakes to Avoid

When evaluating quadratic expressions, there are several common mistakes to avoid:

• Not substituting the value of x correctly: Make sure to substitute the value of x correctly into the expression.
• Not simplifying the expression correctly: Simplify the expression by evaluating the exponent and multiplying the numbers.
• Not checking the units: Check the units of the expression to ensure that they are correct.

Conclusion

Evaluating quadratic expressions is a crucial skill in algebra that helps us find the value of an expression when a variable is replaced by a specific value. By following the steps outlined in this article, we can evaluate quadratic expressions with confidence. Remember to substitute the value of x correctly, simplify the expression correctly, and check the units to avoid common mistakes.

Final Answer

$$

Introduction

In our previous article, we discussed how to evaluate quadratic expressions, with a focus on the quadratic expression $3x^2 - 1$ when $x = 2$. In this article, we will provide a Q&A guide to help you better understand the process of evaluating quadratic expressions.

Q: What is a quadratic expression?

A: A quadratic expression is a polynomial expression of degree two, which means it has a variable raised to the power of two. It is typically written in the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q: How do I evaluate a quadratic expression?

A: To evaluate a quadratic expression, you need to substitute the value of the variable into the expression and simplify. Here are the steps:

1. Substitute the value of the variable into the expression.
2. Simplify the expression by evaluating the exponent and multiplying the numbers.
3. Check the units of the expression to ensure that they are correct.

Q: What if the expression has a negative exponent?

A: If the expression has a negative exponent, you need to follow the rules of exponents. For example, if the expression is $x^{-2}$, you can rewrite it as $\frac{1}{x^2}$.

Q: Can I evaluate a quadratic expression with a variable in the exponent?

A: Yes, you can evaluate a quadratic expression with a variable in the exponent. For example, if the expression is $x^{2x}$, you need to substitute the value of $x$ into the expression and simplify.

Q: How do I handle fractions in a quadratic expression?

A: When handling fractions in a quadratic expression, you need to follow the rules of fractions. For example, if the expression is $\frac{x^2}{2} - 1$, you need to simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Q: Can I evaluate a quadratic expression with a radical in the expression?

A: Yes, you can evaluate a quadratic expression with a radical in the expression. For example, if the expression is $x^2 + \sqrt{2}$, you need to substitute the value of $x$ into the expression and simplify.

Q: What if the expression has a coefficient in front of the variable?

A: If the expression has a coefficient in front of the variable, you need to multiply the coefficient by the variable. For example, if the expression is $2x^2 - 1$, you need to multiply the coefficient $2$ by the variable $x^2$.

Q: Can I evaluate a quadratic expression with a trigonometric function in the expression?

A: Yes, you can evaluate a quadratic expression with a trigonometric function in the expression. For example, if the expression is $\sin^2 x + 2$, you need to substitute the value of $x$ into the expression and simplify.

Conclusion

Evaluating quadratic expressions is a crucial skill in algebra that helps us find the value of an expression when a variable is replaced by a specific value. By following the steps outlined in this article, you can evaluate quadratic expressions with confidence. Remember to substitute the value of the variable correctly, simplify the expression correctly, and check the units to avoid common mistakes.

Final Tips

• Practice, practice, practice: The more you practice evaluating quadratic expressions, the more confident you will become.
• Use a calculator: If you are having trouble evaluating a quadratic expression, try using a calculator to check your work.
• Check your units: Always check the units of the expression to ensure that they are correct.

Common Mistakes to Avoid

• Not substituting the value of the variable correctly: Make sure to substitute the value of the variable correctly into the expression.
• Not simplifying the expression correctly: Simplify the expression by evaluating the exponent and multiplying the numbers.
• Not checking the units: Check the units of the expression to ensure that they are correct.

Final Answer

The final answer is $\boxed{11}$.