Substitute the value of x into the function

Oct 13, 2025 by magicalceylontours.com 52 views

Introduction

Quadratic functions are a fundamental concept in mathematics, and they have numerous applications in various fields, including physics, engineering, and economics. A quadratic function is a polynomial function of degree two, which means the highest power of the variable is two. In this article, we will discuss how to find the value of a quadratic function at a given point. We will use the function $$f(x) = 4x^2 + 2$$ as an example to illustrate the process.

Understanding the Function

The given function is $$f(x) = 4x^2 + 2$$. This is a quadratic function because the highest power of the variable $x$ is two. The coefficient of the squared term is 4, which means the parabola opens upwards. The constant term is 2, which is the y-intercept of the parabola.

Finding the Value of the Function at a Given Point

To find the value of the function at a given point, we need to substitute the value of the point into the function. In this case, we want to find the value of the function at $x = -9$ . We will substitute $x = -9$ into the function and simplify the expression.

Substituting the Value of x into the Function

To find the value of the function at $x = -9$ , we will substitute $x = -9$ into the function:

f(-9) = 4(-9)^2 + 2

Simplifying the Expression

Now, we will simplify the expression by evaluating the squared term and multiplying it by the coefficient:

f(-9) = 4(81) + 2

Evaluating the Expression

Next, we will evaluate the expression by multiplying 4 by 81 and adding 2:

f(-9) = 324 + 2

Final Answer

Finally, we will add 324 and 2 to get the final answer:

f(-9) = 326

Conclusion

In this article, we discussed how to find the value of a quadratic function at a given point. We used the function $$f(x) = 4x^2 + 2$$ as an example to illustrate the process. We substituted the value of the point into the function, simplified the expression, and evaluated it to get the final answer. This process can be applied to any quadratic function to find its value at a given point.

Examples and Applications

Quadratic functions have numerous applications in various fields, including physics, engineering, and economics. Here are a few examples:

Projectile Motion: The trajectory of a projectile under the influence of gravity is a quadratic function.
Optimization: Quadratic functions are used to model optimization problems, such as finding the maximum or minimum of a function.
Signal Processing: Quadratic functions are used in signal processing to filter out noise and extract useful information from signals.

Tips and Tricks

Here are a few tips and tricks to help you find the value of a quadratic function at a given point:

Substitute the value of x into the function: This is the first step in finding the value of a quadratic function at a given point.
Simplify the expression: Simplify the expression by evaluating the squared term and multiplying it by the coefficient.
Evaluate the expression: Evaluate the expression by adding or subtracting the terms.
Check your answer: Check your answer by plugging it back into the original function.

Common Mistakes

Here are a few common mistakes to avoid when finding the value of a quadratic function at a given point:

Not substituting the value of x into the function: This is the most common mistake when finding the value of a quadratic function at a given point.
Not simplifying the expression: Failing to simplify the expression can lead to incorrect answers.
Not evaluating the expression: Failing to evaluate the expression can lead to incorrect answers.
Not checking your answer: Failing to check your answer can lead to incorrect answers.

Conclusion

In conclusion, finding the value of a quadratic function at a given point is a straightforward process that involves substituting the value of the point into the function, simplifying the expression, and evaluating it. By following these steps and avoiding common mistakes, you can find the value of a quadratic function at a given point with ease.

Introduction

In our previous article, we discussed how to find the value of a quadratic function at a given point. We used the function $$f(x) = 4x^2 + 2$$ as an example to illustrate the process. In this article, we will answer some frequently asked questions about finding the value of a quadratic function at a given point.

Q: What is the value of the function $$f(x) = 2x^2 - 3$$ at $x = 5$ ?

A: To find the value of the function at $x = 5$ , we will substitute $x = 5$ into the function:

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

Simplifying the expression, we get:

f(5) = 2(25) - 3

Evaluating the expression, we get:

f(5) = 50 - 3

Finally, we get:

f(5) = 47

Q: What is the value of the function $$f(x) = x^2 + 1$$ at $x = -2$ ?

A: To find the value of the function at $x = -2$ , we will substitute $x = -2$ into the function:

f(-2) = (-2)^2 + 1

Simplifying the expression, we get:

f(-2) = 4 + 1

Evaluating the expression, we get:

f(-2) = 5

Q: What is the value of the function $$f(x) = 3x^2 - 2$$ at $x = 0$ ?

A: To find the value of the function at $x = 0$ , we will substitute $x = 0$ into the function:

f(0) = 3(0)^2 - 2

Simplifying the expression, we get:

f(0) = 0 - 2

Evaluating the expression, we get:

f(0) = -2

Q: How do I find the value of a quadratic function at a given point if the function is in the form $$f(x) = ax^2 + bx + c$$?

A: To find the value of a quadratic function at a given point if the function is in the form $$f(x) = ax^2 + bx + c$$, you will need to substitute the value of the point into the function and simplify the expression. For example, if you want to find the value of the function $$f(x) = 2x^2 + 3x - 1$$ at $x = 4$ , you will need to substitute $x = 4$ into the function:

f(4) = 2(4)^2 + 3(4) - 1

Simplifying the expression, you get:

f(4) = 2(16) + 12 - 1

Evaluating the expression, you get:

f(4) = 32 + 12 - 1

Finally, you get:

f(4) = 43

Q: What is the value of the function $$f(x) = x^2 - 4x + 4$$ at $x = 2$ ?

A: To find the value of the function at $x = 2$ , we will substitute $x = 2$ into the function:

f(2) = (2)^2 - 4(2) + 4

Simplifying the expression, we get:

f(2) = 4 - 8 + 4

Evaluating the expression, we get:

f(2) = 0

Q: How do I find the value of a quadratic function at a given point if the function is in the form $$f(x) = a(x - h)^2 + k$$?

A: To find the value of a quadratic function at a given point if the function is in the form $$f(x) = a(x - h)^2 + k$$, you will need to substitute the value of the point into the function and simplify the expression. For example, if you want to find the value of the function $$f(x) = 2(x - 1)^2 + 3$$ at $x = 3$ , you will need to substitute $x = 3$ into the function:

f(3) = 2(3 - 1)^2 + 3

Simplifying the expression, you get:

f(3) = 2(2)^2 + 3

Evaluating the expression, you get:

f(3) = 2(4) + 3

Finally, you get:

f(3) = 8 + 3

f(3) = 11

Conclusion

In this article, we answered some frequently asked questions about finding the value of a quadratic function at a given point. We provided examples and step-by-step solutions to help you understand the process. By following these steps and practicing with different functions and points, you will become proficient in finding the value of a quadratic function at a given point.