Answer:
The function y=-(x+5)^2+4 is a transformation of the parent function y=x^2. There are three transformations that have been applied to the parent function to obtain the new function:
1. Reflection about the x-axis: The negative sign in front of the function means that the graph of the function has been reflected about the x-axis. This means that every point on the original graph has been reflected across the x-axis to create a new point on the transformed graph.
2. Horizontal shift: The function has been shifted left by 5 units. This means that every point on the original graph has been moved 5 units to the left to create a new point on the transformed graph.
3. Vertical shift: The function has been shifted up by 4 units. This means that every point on the original graph has been moved 4 units up to create a new point on the transformed graph.
Together, these transformations result in a new graph that is a reflection of the parent function about the x-axis, shifted 5 units to the left, and shifted 4 units up. The vertex of the parabola has moved from the origin (0,0) to the point (-5,4). The shape of the parabola remains the same, but its position and orientation have been altered by the transformations.