Finding the Equation of the Vertical Line of Symmetry

Oct 13, 2025 by miodeya.com 131 views

Understanding the Graph of y=|x+2|

The graph of the equation y=|x+2| is a V-shaped graph that opens upwards. This graph is a result of the absolute value function, which is defined as the distance of a number from zero on the number line. The absolute value function is symmetric with respect to a vertical line, and in this case, the equation is y=|x+2|.

What Does Symmetry Mean in This Context?

Symmetry in the context of a graph means that if we were to fold the graph along a particular line, the two halves of the graph would match perfectly. In the case of the graph of y=|x+2|, the vertical line of symmetry is the line that passes through the vertex of the V-shaped graph.

Finding the Equation of the Vertical Line of Symmetry

To find the equation of the vertical line of symmetry, we need to find the x-coordinate of the vertex of the V-shaped graph. The vertex of the graph is the point where the two arms of the V meet. Since the graph is symmetric with respect to a vertical line, the x-coordinate of the vertex is the same as the x-coordinate of the vertical line of symmetry.

The Vertex of the Graph

The vertex of the graph of y=|x+2| is the point where the two arms of the V meet. To find the x-coordinate of the vertex, we need to find the value of x that makes the expression inside the absolute value bars equal to zero. In this case, the expression inside the absolute value bars is x+2, and we need to find the value of x that makes this expression equal to zero.

Solving for x

To solve for x, we need to set the expression inside the absolute value bars equal to zero and solve for x. In this case, we have:

x+2=0

Subtracting 2 from both sides of the equation, we get:

x=-2

The Equation of the Vertical Line of Symmetry

Now that we have found the x-coordinate of the vertex, we can write the equation of the vertical line of symmetry. The equation of a vertical line is of the form x=a, where a is the x-coordinate of the line. In this case, the x-coordinate of the line is -2, so the equation of the vertical line of symmetry is:

x=-2

Conclusion

In conclusion, the graph of y=|x+2| is symmetric with respect to a vertical line. The equation of the vertical line of symmetry is x=-2. This means that if we were to fold the graph along the line x=-2, the two halves of the graph would match perfectly.

Key Takeaways

The graph of y=|x+2| is a V-shaped graph that opens upwards.
The graph is symmetric with respect to a vertical line.
The equation of the vertical line of symmetry is x=-2.
The x-coordinate of the vertex of the graph is the same as the x-coordinate of the vertical line of symmetry.

Frequently Asked Questions

What is the equation of the vertical line of symmetry for the graph of y=|x+2|?
The equation of the vertical line of symmetry is x=-2.
What is the x-coordinate of the vertex of the graph of y=|x+2|?
The x-coordinate of the vertex is -2.

Understanding the Graph of y=|x+2|

Q&A: The Graph of y=|x+2|

Q: What is the equation of the vertical line of symmetry for the graph of y=|x+2|?

A: The equation of the vertical line of symmetry is x=-2.

Q: What is the x-coordinate of the vertex of the graph of y=|x+2|?

A: The x-coordinate of the vertex is -2.

Q: Why is the graph of y=|x+2| symmetric with respect to a vertical line?

A: The graph of y=|x+2| is symmetric with respect to a vertical line because the absolute value function is symmetric with respect to a vertical line.

Q: What is the significance of the vertex of the graph of y=|x+2|?

A: The vertex of the graph of y=|x+2| is the point where the two arms of the V meet. The x-coordinate of the vertex is the same as the x-coordinate of the vertical line of symmetry.

Q: How do you find the equation of the vertical line of symmetry for the graph of y=|x+2|?

A: To find the equation of the vertical line of symmetry, you need to find the x-coordinate of the vertex of the graph. The x-coordinate of the vertex is the same as the x-coordinate of the vertical line of symmetry.

Q: What is the relationship between the graph of y=|x+2| and the absolute value function?

A: The graph of y=|x+2| is a result of the absolute value function, which is defined as the distance of a number from zero on the number line.

Q: What is the significance of the absolute value function in the context of the graph of y=|x+2|?

A: The absolute value function is symmetric with respect to a vertical line, and in this case, the equation is y=|x+2|.

Common Misconceptions

The graph of y=|x+2| is not symmetric with respect to a horizontal line.
The equation of the vertical line of symmetry is x=2, not x=-2.
The x-coordinate of the vertex of the graph of y=|x+2| is not -2, but rather 2.

Conclusion

Key Takeaways

The graph of y=|x+2| is a V-shaped graph that opens upwards.
The graph is symmetric with respect to a vertical line.
The equation of the vertical line of symmetry is x=-2.
The x-coordinate of the vertex of the graph is the same as the x-coordinate of the vertical line of symmetry.

Resources

Khan Academy: Absolute Value Functions
Mathway: Graphing Absolute Value Functions
Wolfram Alpha: Symmetry in Graphs