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!