Question
If the graph of \( y = -x^2 \) is obtained by reflecting \( y = x^2 \) across the x-axis, what will be the coordinates of the vertex after the reflection?
Ask by Thornton Mcdonald. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The vertex remains at \((0,\ 0)\) after reflecting \( y = x^2 \) across the x-axis.
Solution
The graph of \( y = x^2 \) has its vertex at the point \( (0, 0) \).
When you reflect this graph across the x-axis, every point \( (x, y) \) on the original graph is transformed to \( (x, -y) \). Specifically for the vertex:
- Original vertex: \( (0, 0) \)
- After reflection: \( (0, -0) \), which simplifies to \( (0, 0) \)
Therefore, the coordinates of the vertex remain unchanged after the reflection.
**Answer:** \((0,\ 0)\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
The graph of \( y = x^2 \) has its vertex at the origin, which is the point \( (0, 0) \). When we reflect this graph across the x-axis, we change the sign of the y-coordinates of the points on the graph. Therefore, the coordinates of the vertex after the reflection will remain at the same x-coordinate, but the y-coordinate changes from 0 to 0. Thus, the coordinates of the vertex after the reflection remain \( (0, 0) \).
