To find the graph of \( y = -f(x) \) given \( f(x) = (x+3)^2 \), we first recognize that the function \( f(x) \) is a parabola that opens upwards with its vertex at the point (-3, 0) since the vertex form of a parabola is \( f(x) = a(x-h)^2 + k \), where (h, k) is the vertex.
The graph of \( y = -f(x) \) will reflect this parabola over the x-axis. Therefore, it will open downwards, and its vertex will remain at the same horizontal position (-3) but will move down vertically to (-3, 0), resulting in the vertex being at (-3, 0).
To summarize:
- The graph of \( f(x) = (x+3)^2 \) opens upwards.
- The graph of \( y = -f(x) \) opens downwards and has the vertex at (-3, 0).
In conclusion, the graph of \( y = -f(x) \) will be an inverted parabola centered at (-3, 0). You will need to look for the option that depicts a downward opening parabola with that vertex.
Since I don't have the actual graphs or options in front of me, please identify and choose the graph that matches this description.
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