Question

Use the to answer the question.

Two parabolas and two inverted parabolas, all with arrows on both ends, are drawn on a coordinate plane with the x-axis from negative 6 to 6 and the y-axis from negative 6 to 6, both in increments of 1.

Given the graph of f(x)=(x+3)2
, which of the options is the graph of y=−f(x)
?

(1 point)
The graph of y=−f(x)
is option
.

Answer 1

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.