Evaluate The Given Expression For $x = -5$:$-2x^2 - 5x - 7$The Answer Is $ □ \square □ [/tex].

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students to master. In this article, we will focus on evaluating a given quadratic expression for a specific value of x. We will break down the process into manageable steps and provide a clear explanation of each step.

Understanding the Expression

The given expression is $-2x^2 - 5x - 7$. This is a quadratic expression, which means it has a squared variable (x^2) and a linear term (5x). The constant term is -7.

Evaluating the Expression for x = -5

To evaluate the expression for x = -5, we need to substitute x = -5 into the expression. This means we will replace every instance of x with -5.

Step 1: Substitute x = -5 into the Expression

−2x2−5x−7-2x^2 - 5x - 7

Replace x with -5:

−2(−5)2−5(−5)−7-2(-5)^2 - 5(-5) - 7

Step 2: Simplify the Expression

Now that we have substituted x = -5, we need to simplify the expression. We will start by evaluating the squared term:

(−5)2=25(-5)^2 = 25

So, the expression becomes:

−2(25)−5(−5)−7-2(25) - 5(-5) - 7

Step 3: Multiply the Coefficients

Next, we need to multiply the coefficients of the squared term and the linear term:

−2(25)=−50-2(25) = -50

−5(−5)=25-5(-5) = 25

So, the expression becomes:

−50+25−7-50 + 25 - 7

Step 4: Combine Like Terms

Now, we need to combine the like terms:

−50+25=−25-50 + 25 = -25

So, the expression becomes:

−25−7-25 - 7

Step 5: Simplify the Expression

Finally, we need to simplify the expression by combining the constant terms:

−25−7=−32-25 - 7 = -32

Conclusion

In this article, we evaluated the given quadratic expression for x = -5. We broke down the process into manageable steps and provided a clear explanation of each step. By following these steps, we were able to simplify the expression and find the final value.

Final Answer

The final answer is: −32\boxed{-32}

Frequently Asked Questions

Q: What is a quadratic expression?

A: A quadratic expression is a polynomial expression of degree two, which means it has a squared variable and a linear term.

Q: How do I evaluate a quadratic expression for a specific value of x?

A: To evaluate a quadratic expression for a specific value of x, you need to substitute x into the expression and simplify the resulting expression.

Q: What is the difference between a quadratic expression and a linear expression?

A: A quadratic expression has a squared variable, while a linear expression does not have a squared variable.

Additional Resources

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article, you can evaluate quadratic expressions for specific values of x. Remember to substitute x into the expression, simplify the resulting expression, and combine like terms to find the final value.

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Introduction

In our previous article, we discussed how to evaluate a quadratic expression for a specific value of x. In this article, we will provide a Q&A guide to help you better understand the process of evaluating algebraic expressions.

Frequently Asked Questions

Q: What is a quadratic expression?

A: A quadratic expression is a polynomial expression of degree two, which means it has a squared variable and a linear term.

Q: How do I evaluate a quadratic expression for a specific value of x?

A: To evaluate a quadratic expression for a specific value of x, you need to substitute x into the expression and simplify the resulting expression.

Q: What is the difference between a quadratic expression and a linear expression?

A: A quadratic expression has a squared variable, while a linear expression does not have a squared variable.

Q: How do I simplify a quadratic expression?

A: To simplify a quadratic expression, you need to combine like terms and perform any necessary operations, such as multiplication or addition.

Q: What is the order of operations when evaluating a quadratic expression?

A: The order of operations is:

  1. Parentheses: Evaluate any expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I handle negative numbers when evaluating a quadratic expression?

A: When evaluating a quadratic expression with negative numbers, you need to follow the order of operations and perform any necessary operations, such as multiplication or addition.

Q: Can I use a calculator to evaluate a quadratic expression?

A: Yes, you can use a calculator to evaluate a quadratic expression. However, it's always a good idea to double-check your work and make sure you understand the process of evaluating the expression.

Q: What are some common mistakes to avoid when evaluating a quadratic expression?

A: Some common mistakes to avoid when evaluating a quadratic expression include:

  • Not following the order of operations
  • Not combining like terms
  • Not performing necessary operations, such as multiplication or addition
  • Not checking your work

Additional Tips and Tricks

  • Make sure to read the problem carefully and understand what is being asked.
  • Use a pencil and paper to work out the problem, rather than relying on a calculator.
  • Check your work by plugging in a simple value for x and evaluating the expression.
  • Use a calculator to check your work, but make sure to understand the process of evaluating the expression.

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article and avoiding common mistakes, you can become more confident and proficient in evaluating quadratic expressions. Remember to always follow the order of operations, combine like terms, and perform necessary operations to find the final value.

Final Answer

The final answer is: −32\boxed{-32}

Frequently Asked Questions (continued)

Q: What is the difference between a quadratic equation and a quadratic expression?

A: A quadratic equation is an equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants. A quadratic expression is a polynomial expression of degree two, which means it has a squared variable and a linear term.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to find the values of x that satisfy the equation. You can use various methods, such as factoring, the quadratic formula, or graphing.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that can be used to solve quadratic equations. It is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: How do I use the quadratic formula?

A: To use the quadratic formula, you need to plug in the values of a, b, and c into the formula and simplify.

Additional Resources

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article and avoiding common mistakes, you can become more confident and proficient in evaluating quadratic expressions. Remember to always follow the order of operations, combine like terms, and perform necessary operations to find the final value.