Given The Function $f(x) = -5x^2 - X + 20$, Find $f(3$\].A. $-28$ B. 64 C. 62 D. $-13$

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Introduction

In mathematics, a quadratic function is a polynomial function of degree two, which means the highest power of the variable is two. These functions are commonly represented in the form of f(x) = ax^2 + bx + c, where a, b, and c are constants. In this article, we will focus on evaluating a quadratic function given by f(x) = -5x^2 - x + 20 at a specific value of x, namely x = 3.

Understanding the Quadratic Function

The given quadratic function is f(x) = -5x^2 - x + 20. To evaluate this function at x = 3, we need to substitute x = 3 into the function and simplify the expression.

Substituting x = 3 into the Function

To find f(3), we substitute x = 3 into the function f(x) = -5x^2 - x + 20.

f(3) = -5(3)^2 - 3 + 20

Simplifying the Expression

Now, let's simplify the expression by evaluating the exponent and performing the arithmetic operations.

f(3) = -5(9) - 3 + 20
f(3) = -45 - 3 + 20
f(3) = -48 + 20
f(3) = -28

Conclusion

In this article, we evaluated the quadratic function f(x) = -5x^2 - x + 20 at x = 3. By substituting x = 3 into the function and simplifying the expression, we found that f(3) = -28. This result is consistent with option A.

Key Takeaways

  • A quadratic function is a polynomial function of degree two, represented in the form of f(x) = ax^2 + bx + c.
  • To evaluate a quadratic function at a specific value of x, substitute x into the function and simplify the expression.
  • When evaluating a quadratic function, make sure to follow the order of operations (PEMDAS) to simplify the expression correctly.

Practice Problems

  1. Evaluate the quadratic function f(x) = 2x^2 + 3x - 1 at x = 2.
  2. Find the value of f(-2) for the quadratic function f(x) = -x^2 + 4x - 3.
  3. Evaluate the quadratic function f(x) = x^2 - 5x + 6 at x = 1.

Solutions

  1. f(2) = 2(2)^2 + 3(2) - 1 f(2) = 2(4) + 6 - 1 f(2) = 8 + 6 - 1 f(2) = 13
  2. f(-2) = -(-2)^2 + 4(-2) - 3 f(-2) = -4 - 8 - 3 f(-2) = -15
  3. f(1) = (1)^2 - 5(1) + 6 f(1) = 1 - 5 + 6 f(1) = 2
    Evaluating Quadratic Functions: A Q&A Guide =====================================================

Introduction

In our previous article, we discussed how to evaluate a quadratic function at a specific value of x. In this article, we will provide a Q&A guide to help you better understand the concept of evaluating quadratic functions.

Q: What is a quadratic function?

A: A quadratic function is a polynomial function of degree two, represented in the form of f(x) = ax^2 + bx + c, where a, b, and c are constants.

Q: How do I evaluate a quadratic function at a specific value of x?

A: To evaluate a quadratic function at a specific value of x, substitute x into the function and simplify the expression. Make sure to follow the order of operations (PEMDAS) to simplify the expression correctly.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an expression. The acronym PEMDAS stands for:

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

Q: How do I simplify a quadratic expression?

A: To simplify a quadratic expression, follow these steps:

  1. Evaluate any exponential expressions.
  2. Multiply and divide any terms from left to right.
  3. Add and subtract any terms from left to right.

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

A: Here are some common mistakes to avoid when evaluating quadratic functions:

  • Not following the order of operations (PEMDAS).
  • Not simplifying the expression correctly.
  • Not evaluating any exponential expressions.
  • Not multiplying and dividing any terms from left to right.

Q: How do I check my work when evaluating a quadratic function?

A: To check your work when evaluating a quadratic function, follow these steps:

  1. Plug the value of x back into the original function.
  2. Simplify the expression using the order of operations (PEMDAS).
  3. Compare your answer to the original expression.

Q: What are some real-world applications of quadratic functions?

A: Quadratic functions have many real-world applications, including:

  • Modeling the trajectory of a projectile.
  • Finding the maximum or minimum value of a function.
  • Solving problems involving optimization.

Conclusion

Evaluating quadratic functions is an important concept in mathematics. By following the steps outlined in this article, you can confidently evaluate quadratic functions and apply them to real-world problems.

Practice Problems

  1. Evaluate the quadratic function f(x) = 2x^2 + 3x - 1 at x = 2.
  2. Find the value of f(-2) for the quadratic function f(x) = -x^2 + 4x - 3.
  3. Evaluate the quadratic function f(x) = x^2 - 5x + 6 at x = 1.

Solutions

  1. f(2) = 2(2)^2 + 3(2) - 1 f(2) = 2(4) + 6 - 1 f(2) = 8 + 6 - 1 f(2) = 13
  2. f(-2) = -(-2)^2 + 4(-2) - 3 f(-2) = -4 - 8 - 3 f(-2) = -15
  3. f(1) = (1)^2 - 5(1) + 6 f(1) = 1 - 5 + 6 f(1) = 2