Which Of The Following Is The Vertex Of Y = − F ( − X Y=-f(-x Y = − F ( − X ] If The Original Function Has A Vertex Of ( − 9 , − 8 (-9,-8 ( − 9 , − 8 ]?A. ( − 9 , 8 (-9, 8 ( − 9 , 8 ] B. ( 9 , 8 (9, 8 ( 9 , 8 ] C. ( 9 , − 8 (9, -8 ( 9 , − 8 ] D. ( − 9 , − 8 (-9, -8 ( − 9 , − 8 ]

Mar 12, 2025 by ADMIN 283 views

**Vertex Transformation in Functions**

Understanding Vertex Transformation

In mathematics, particularly in algebra and geometry, the vertex of a function is a crucial point that represents the minimum or maximum value of the function. When a function undergoes a transformation, its vertex also undergoes a transformation. In this article, we will explore how the vertex of a function changes when it is reflected across the y-axis.

Original Function and Vertex

The original function is given as $y = f(x)$ . The vertex of this function is $(-9, -8)$ . This means that the minimum or maximum value of the function occurs at the point $(-9, -8)$ .

Reflection Across the Y-Axis

When a function is reflected across the y-axis, the x-coordinate of the vertex changes sign. In other words, if the original vertex is at $(-9, -8)$ , the new vertex will be at $(9, -8)$ .

New Function and Vertex

The new function is given as $y = -f(-x)$ . To find the vertex of this function, we need to substitute $-x$ into the original function and then reflect the resulting function across the y-axis.

Step-by-Step Solution

Substitute $-x$ into the original function: $y = f(-x)$
Reflect the resulting function across the y-axis: $y = -f(-x)$
Find the vertex of the new function: The vertex of the new function is $(9, -8)$ .

Conclusion

In conclusion, when a function undergoes a reflection across the y-axis, the x-coordinate of the vertex changes sign. Therefore, the vertex of the new function $y = -f(-x)$ is $(9, -8)$ .

Answer

The correct answer is C. $(9, -8)$ .

Explanation

The other options are incorrect because:

A. $(-9, 8)$ is the reflection of the original vertex across the x-axis, not the y-axis.
B. $(9, 8)$ is the reflection of the original vertex across the x-axis, not the y-axis.
D. $(-9, -8)$ is the original vertex, not the new vertex.

Example Use Case

Suppose we have a function $y = f(x)$ with a vertex at $(-9, -8)$ . If we want to reflect this function across the y-axis, we can use the new function $y = -f(-x)$ and find its vertex at $(9, -8)$ .

Tips and Tricks

When reflecting a function across the y-axis, the x-coordinate of the vertex changes sign.
When reflecting a function across the x-axis, the y-coordinate of the vertex changes sign.
To find the vertex of a function, we need to find the minimum or maximum value of the function.

Conclusion

Frequently Asked Questions

In this article, we will answer some frequently asked questions about vertex transformation in functions.

Q: What is vertex transformation?

A: Vertex transformation is the process of changing the vertex of a function when it undergoes a transformation. This can include reflections, translations, and other types of transformations.

Q: What happens to the vertex when a function is reflected across the y-axis?

A: When a function is reflected across the y-axis, the x-coordinate of the vertex changes sign. For example, if the original vertex is at $(-9, -8)$ , the new vertex will be at $(9, -8)$ .

Q: What happens to the vertex when a function is reflected across the x-axis?

A: When a function is reflected across the x-axis, the y-coordinate of the vertex changes sign. For example, if the original vertex is at $(-9, -8)$ , the new vertex will be at $(-9, 8)$ .

Q: How do I find the vertex of a function after it has undergone a transformation?

A: To find the vertex of a function after it has undergone a transformation, you need to apply the transformation to the original function and then find the minimum or maximum value of the resulting function.

Q: What is the difference between a reflection and a translation?

A: A reflection is a transformation that flips a function over a line, while a translation is a transformation that moves a function up or down or left or right.

Q: Can you give an example of a function that has undergone a vertex transformation?

A: Yes, consider the function $y = f(x)$ with a vertex at $(-9, -8)$ . If we want to reflect this function across the y-axis, we can use the new function $y = -f(-x)$ and find its vertex at $(9, -8)$ .

Q: How do I determine if a function has undergone a vertex transformation?

A: To determine if a function has undergone a vertex transformation, you need to look for changes in the x or y coordinates of the vertex. If the x-coordinate has changed sign, the function has been reflected across the y-axis. If the y-coordinate has changed sign, the function has been reflected across the x-axis.

Q: Can you give an example of a function that has undergone a translation?

A: Yes, consider the function $y = f(x)$ with a vertex at $(-9, -8)$ . If we want to move this function up by 3 units, we can use the new function $y = f(x) + 3$ and find its vertex at $(-9, 1)$ .

Q: How do I determine if a function has undergone a translation?

A: To determine if a function has undergone a translation, you need to look for changes in the y-coordinate of the vertex. If the y-coordinate has changed, the function has been translated.

Conclusion

In conclusion, vertex transformation is an important concept in mathematics that can help us understand how functions change when they undergo transformations. By answering these frequently asked questions, we hope to have provided a better understanding of vertex transformation and its applications.

Tips and Tricks

When reflecting a function across the y-axis, the x-coordinate of the vertex changes sign.
When reflecting a function across the x-axis, the y-coordinate of the vertex changes sign.
To find the vertex of a function after it has undergone a transformation, you need to apply the transformation to the original function and then find the minimum or maximum value of the resulting function.
To determine if a function has undergone a vertex transformation, you need to look for changes in the x or y coordinates of the vertex.
To determine if a function has undergone a translation, you need to look for changes in the y-coordinate of the vertex.