https://file.aiquickdraw.com/mathbot/file/1726970505238iew90u2u.jpg

The image presents a problem regarding the transformation of a quadratic function graph. Here's a breakdown of the tasks based on the image:

1. **Initial Graph**: Start by sketching the quadratic function \( y = -x^2 \), which is a downward-opening parabola.
   
2. **Translation**: Apply the translation defined by the vector \( \left( -2, 4 \right) \). This moves the graph 2 units to the left and 4 units up.
   
3. **Reflection**: Reflect the translated graph across the horizontal axis (x-axis). This changes the graph's orientation.
   
4. **Dilation**: From the reflected graph, apply a dilation by a factor of 3 along the x-axis. This stretches the graph horizontally.
   
5. **Rotation**: Rotate the resulting graph 90 degrees counterclockwise about the origin \( (0, 0) \).

Would you like to go through each transformation with detailed explanations or a sketch of the graph?

Here are five related questions to further explore the concepts:

1. What is the effect of translating a graph by the vector \( (-2, 4) \)?
2. How does reflection across the x-axis affect the function's graph?
3. What changes occur when a graph is dilated by a factor of 3 along the x-axis?
4. How would a rotation of 90° around the origin alter the graph's shape and orientation?
5. How would the process differ if we rotated the graph by 90° clockwise instead?

**Tip**: For geometric transformations, always visualize how each step affects key points (like the vertex or intercepts) to ensure accuracy!

Jika lengkungan jembatan tersebut kita misalkan suatu fungsi kuadrat y = -x^2, maka tentukan minimal 2 bentuk grafik fungsi tersebut dengan koordinat yang berbeda, selanjutnya transformasikan gambar grafik tersebut sesuai dengan aturan berikut.

Learn how to apply geometric transformations to the quadratic function y = -x^2. This problem covers translation by (-2, 4), reflection across the x-axis, dilation by a factor of 3, and rotation by 90 degrees. Suitable for students in Grades 10-12.

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