The Graph Of The Function $f(x)=x^2-4x+6$ Is Shown Here. What Is Its Axis Of Symmetry?A. $x=0$B. \$x=2$[/tex\]C. $x=6$D. $x=-2$
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Introduction
In mathematics, the axis of symmetry is a line that divides a quadratic function into two symmetrical parts. It is a crucial concept in algebra and is used to determine the vertex of a parabola. In this article, we will discuss the axis of symmetry of a quadratic function and how to find it.
What is the Axis of Symmetry?
The axis of symmetry is a vertical line that passes through the vertex of a parabola. It is denoted by the equation x = a, where a is the x-coordinate of the vertex. The axis of symmetry is a line of symmetry, meaning that if we were to fold the parabola along this line, the two halves would match perfectly.
How to Find the Axis of Symmetry
To find the axis of symmetry of a quadratic function, we need to find the x-coordinate of the vertex. The x-coordinate of the vertex can be found using the formula:
x = -b / 2a
where a and b are the coefficients of the quadratic function.
Example
Let's consider the quadratic function f(x) = x^2 - 4x + 6. To find the axis of symmetry, we need to find the x-coordinate of the vertex. Using the formula, we get:
x = -(-4) / 2(1) x = 4 / 2 x = 2
Therefore, the axis of symmetry of the quadratic function f(x) = x^2 - 4x + 6 is x = 2.
Conclusion
In conclusion, the axis of symmetry is a line that divides a quadratic function into two symmetrical parts. It is a crucial concept in algebra and is used to determine the vertex of a parabola. To find the axis of symmetry, we need to find the x-coordinate of the vertex using the formula x = -b / 2a.
The Graph of the Function
The graph of the function f(x) = x^2 - 4x + 6 is shown below:
The Axis of Symmetry of the Graph
The axis of symmetry of the graph is the vertical line that passes through the vertex of the parabola. In this case, the axis of symmetry is x = 2.
Final Answer
The final answer is x = 2.
Discussion
The axis of symmetry is a crucial concept in algebra and is used to determine the vertex of a parabola. It is a line of symmetry, meaning that if we were to fold the parabola along this line, the two halves would match perfectly. In this article, we discussed the axis of symmetry of a quadratic function and how to find it. We also provided an example of how to find the axis of symmetry of a quadratic function.
Related Topics
- Vertex of a Parabola: The vertex of a parabola is the highest or lowest point on the graph. It is the point where the axis of symmetry intersects the parabola.
- Quadratic Functions: Quadratic functions are functions of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
- Graphing Quadratic Functions: Graphing quadratic functions involves plotting the points on the graph and drawing a smooth curve through them.
References
- Algebra: Algebra is a branch of mathematics that deals with the study of variables and their relationships.
- Geometry: Geometry is a branch of mathematics that deals with the study of shapes and their properties.
- Calculus: Calculus is a branch of mathematics that deals with the study of rates of change and accumulation.
Conclusion
In conclusion, the axis of symmetry is a line that divides a quadratic function into two symmetrical parts. It is a crucial concept in algebra and is used to determine the vertex of a parabola. To find the axis of symmetry, we need to find the x-coordinate of the vertex using the formula x = -b / 2a.
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Introduction
In our previous article, we discussed the axis of symmetry of a quadratic function and how to find it. In this article, we will provide a Q&A guide to help you understand the concept of the axis of symmetry better.
Q: What is the axis of symmetry?
A: The axis of symmetry is a vertical line that passes through the vertex of a parabola. It is a line of symmetry, meaning that if we were to fold the parabola along this line, the two halves would match perfectly.
Q: How do I find the axis of symmetry of a quadratic function?
A: To find the axis of symmetry of a quadratic function, you need to find the x-coordinate of the vertex. The x-coordinate of the vertex can be found using the formula:
x = -b / 2a
where a and b are the coefficients of the quadratic function.
Q: What is the formula for finding the axis of symmetry?
A: The formula for finding the axis of symmetry is:
x = -b / 2a
Q: How do I use the formula to find the axis of symmetry?
A: To use the formula, you need to identify the values of a and b in the quadratic function. Then, plug these values into the formula and solve for x.
Q: What if the quadratic function is in the form f(x) = ax^2 + c?
A: If the quadratic function is in the form f(x) = ax^2 + c, then the axis of symmetry is x = 0.
Q: Can the axis of symmetry be a horizontal line?
A: No, the axis of symmetry is always a vertical line.
Q: Can the axis of symmetry be a diagonal line?
A: No, the axis of symmetry is always a vertical line.
Q: How do I graph a quadratic function with an axis of symmetry?
A: To graph a quadratic function with an axis of symmetry, you need to find the vertex of the parabola and plot it on the graph. Then, draw a vertical line through the vertex to represent the axis of symmetry.
Q: What is the significance of the axis of symmetry?
A: The axis of symmetry is significant because it helps us to determine the vertex of a parabola. It is also used to graph quadratic functions.
Q: Can the axis of symmetry be used to solve quadratic equations?
A: Yes, the axis of symmetry can be used to solve quadratic equations. By finding the axis of symmetry, you can determine the vertex of the parabola and use it to solve the equation.
Q: How do I use the axis of symmetry to solve quadratic equations?
A: To use the axis of symmetry to solve quadratic equations, you need to find the axis of symmetry and then use it to determine the vertex of the parabola. Then, use the vertex to solve the equation.
Conclusion
In conclusion, the axis of symmetry is a crucial concept in algebra and is used to determine the vertex of a parabola. It is a line of symmetry, meaning that if we were to fold the parabola along this line, the two halves would match perfectly. We hope that this Q&A guide has helped you to understand the concept of the axis of symmetry better.
Related Topics
- Vertex of a Parabola: The vertex of a parabola is the highest or lowest point on the graph. It is the point where the axis of symmetry intersects the parabola.
- Quadratic Functions: Quadratic functions are functions of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
- Graphing Quadratic Functions: Graphing quadratic functions involves plotting the points on the graph and drawing a smooth curve through them.
References
- Algebra: Algebra is a branch of mathematics that deals with the study of variables and their relationships.
- Geometry: Geometry is a branch of mathematics that deals with the study of shapes and their properties.
- Calculus: Calculus is a branch of mathematics that deals with the study of rates of change and accumulation.
Conclusion
In conclusion, the axis of symmetry is a crucial concept in algebra and is used to determine the vertex of a parabola. It is a line of symmetry, meaning that if we were to fold the parabola along this line, the two halves would match perfectly. We hope that this Q&A guide has helped you to understand the concept of the axis of symmetry better.