Name: $\qquad$ Date: $\qquad$3. Make A Table Of Values For The Function $f(x) = X^2 - 2$.$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 3 &
Introduction
In mathematics, a quadratic function is a polynomial function of degree two, which means the highest power of the variable is two. The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants. In this article, we will explore the quadratic function f(x) = x^2 - 2 and create a table of values to understand its behavior.
Understanding the Function
The given function is f(x) = x^2 - 2. This function has a leading coefficient of 1, which means the parabola opens upwards. The vertex of the parabola is at (0, -2), which is the minimum point of the function.
Creating a Table of Values
To create a table of values for the function f(x) = x^2 - 2, we need to substitute different values of x into the function and calculate the corresponding values of y. Here is the table of values:
| x | y |
|---|---|
| -1 | 3 |
| 0 | -2 |
| 1 | 1 |
| 2 | 6 |
| 3 | 13 |
Analyzing the Table of Values
From the table of values, we can observe the following:
- The function is increasing as x increases.
- The function has a minimum point at x = 0, where y = -2.
- The function is symmetric about the y-axis.
Graphing the Function
To visualize the function, we can graph it using the table of values. The graph of the function f(x) = x^2 - 2 is a parabola that opens upwards. The vertex of the parabola is at (0, -2), which is the minimum point of the function.
Conclusion
In this article, we explored the quadratic function f(x) = x^2 - 2 and created a table of values to understand its behavior. We analyzed the table of values and observed that the function is increasing as x increases, has a minimum point at x = 0, and is symmetric about the y-axis. We also graphed the function to visualize its behavior.
Discussion
The quadratic function f(x) = x^2 - 2 is a simple example of a quadratic function. However, it has many real-world applications, such as modeling the motion of objects under the influence of gravity or the growth of populations. The table of values and graph of the function provide valuable insights into its behavior and can be used to make predictions and decisions.
Table of Values
| x | y |
|---|---|
| -1 | 3 |
| 0 | -2 |
| 1 | 1 |
| 2 | 6 |
| 3 | 13 |
Graph of the Function
The graph of the function f(x) = x^2 - 2 is a parabola that opens upwards. The vertex of the parabola is at (0, -2), which is the minimum point of the function.
Real-World Applications
The quadratic function f(x) = x^2 - 2 has many real-world applications, such as:
- Modeling the motion of objects under the influence of gravity
- Modeling the growth of populations
- Designing curves and shapes
- Solving optimization problems
Conclusion
Introduction
In our previous article, we explored the quadratic function f(x) = x^2 - 2 and created a table of values to understand its behavior. In this article, we will answer some frequently asked questions about the quadratic function f(x) = x^2 - 2.
Q: What is the vertex of the parabola?
A: The vertex of the parabola is at (0, -2), which is the minimum point of the function.
Q: Is the function increasing or decreasing?
A: The function is increasing as x increases.
Q: Is the function symmetric about the y-axis?
A: Yes, the function is symmetric about the y-axis.
Q: What is the value of the function at x = 1?
A: The value of the function at x = 1 is 1.
Q: What is the value of the function at x = -1?
A: The value of the function at x = -1 is 3.
Q: How can I use the quadratic function f(x) = x^2 - 2 in real-world applications?
A: The quadratic function f(x) = x^2 - 2 can be used to model the motion of objects under the influence of gravity, model the growth of populations, design curves and shapes, and solve optimization problems.
Q: Can I graph the function using a calculator or computer software?
A: Yes, you can graph the function using a calculator or computer software such as Desmos, GeoGebra, or Mathematica.
Q: How can I find the equation of the parabola?
A: The equation of the parabola is f(x) = x^2 - 2.
Q: What is the domain and range of the function?
A: The domain of the function is all real numbers, and the range of the function is all real numbers greater than or equal to -2.
Q: Can I use the quadratic function f(x) = x^2 - 2 to solve optimization problems?
A: Yes, you can use the quadratic function f(x) = x^2 - 2 to solve optimization problems.
Q: How can I use the quadratic function f(x) = x^2 - 2 to model the motion of objects under the influence of gravity?
A: You can use the quadratic function f(x) = x^2 - 2 to model the motion of objects under the influence of gravity by using the equation of motion: s(t) = s0 + v0t + (1/2)gt^2, where s(t) is the position of the object at time t, s0 is the initial position, v0 is the initial velocity, and g is the acceleration due to gravity.
Conclusion
In conclusion, the quadratic function f(x) = x^2 - 2 is a simple yet powerful tool for modeling and analyzing real-world phenomena. We hope that this Q&A article has provided you with a better understanding of the function and its applications.
Frequently Asked Questions
- What is the vertex of the parabola?
- Is the function increasing or decreasing?
- Is the function symmetric about the y-axis?
- What is the value of the function at x = 1?
- What is the value of the function at x = -1?
- How can I use the quadratic function f(x) = x^2 - 2 in real-world applications?
- Can I graph the function using a calculator or computer software?
- How can I find the equation of the parabola?
- What is the domain and range of the function?
- Can I use the quadratic function f(x) = x^2 - 2 to solve optimization problems?
- How can I use the quadratic function f(x) = x^2 - 2 to model the motion of objects under the influence of gravity?
Answers
- The vertex of the parabola is at (0, -2).
- The function is increasing as x increases.
- Yes, the function is symmetric about the y-axis.
- The value of the function at x = 1 is 1.
- The value of the function at x = -1 is 3.
- The quadratic function f(x) = x^2 - 2 can be used to model the motion of objects under the influence of gravity, model the growth of populations, design curves and shapes, and solve optimization problems.
- Yes, you can graph the function using a calculator or computer software.
- The equation of the parabola is f(x) = x^2 - 2.
- The domain of the function is all real numbers, and the range of the function is all real numbers greater than or equal to -2.
- Yes, you can use the quadratic function f(x) = x^2 - 2 to solve optimization problems.
- You can use the quadratic function f(x) = x^2 - 2 to model the motion of objects under the influence of gravity by using the equation of motion: s(t) = s0 + v0t + (1/2)gt^2.