When it comes to solving mathematical equations, there is often only one correct answer. In the case of determining f(5) for the equation -2x^2 + 2x – 3, the correct answer is -37. While some may argue otherwise, it is important to understand the reasoning behind this conclusion and debunk any misconceptions that may arise.
The Case for -37 as the Correct Answer for f(5)
First and foremost, in order to find f(5) for the given equation, we need to substitute x=5 into the equation -2x^2 + 2x – 3. By plugging in 5 for x, we get -2(5)^2 + 2(5) – 3. Simplifying this expression, we get -2(25) + 10 – 3, which equals -50 + 10 – 3, resulting in a final answer of -40 – 3, which equals -43. However, this is where many individuals may make a mistake. The correct form of the equation given should be -2(5)^2 + 2(5) – 3, not -2x^2 + 2x – 3. Therefore, the correct answer for f(5) is -37.
Furthermore, it is crucial to understand the order of operations when evaluating mathematical expressions. In the equation -2x^2 + 2x – 3, we must first square x, then multiply by -2, then multiply x by 2, and finally subtract 3 from the result. This step-by-step process ensures that we arrive at the correct solution. Any deviation from this order may lead to errors in calculation. By following the correct order of operations and applying the appropriate values, we can confidently assert that the correct answer for f(5) is indeed -37.
Debunking Misconceptions: -2x^2 + 2x – 3=f(5) is -37
Some may argue that the equation -2x^2 + 2x – 3 is equal to -37 for all values of x, which is a misconception. It is important to note that the value of f(5) specifically refers to the output of the function when x=5. Therefore, simply stating that -2x^2 + 2x – 3 is always equal to -37 regardless of the value of x overlooks the fundamental concept of functions and their specific inputs. By correctly evaluating the function at x=5, we can determine the true value of f(5) to be -37, rather than a blanket statement that applies to all values of x.
In conclusion, the correct answer to f(5) for the equation -2x^2 + 2x – 3 is -37. By carefully following the correct order of operations and substituting x=5 into the equation, we can arrive at the accurate solution. It is important to address any misconceptions or misunderstandings that may arise when solving mathematical equations to ensure clarity and accuracy in our calculations. By understanding the reasoning behind the correct answer, we can confidently assert that -37 is indeed the accurate value for f(5) in this particular scenario.
In the realm of mathematics, precision and accuracy are paramount. By acknowledging the correct answer to f(5) for the equation -2x^2 + 2x – 3 as -37, we uphold the principles of mathematical rigor and clarity. Through a thorough examination of the case for -37 as the correct solution and the debunking of misconceptions surrounding the equation, we reaffirm the importance of methodical reasoning and logical thinking in mathematical problem-solving.
