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 that \( f(x) = (x + 3)^2 \), we first note what the graph of \( f(x) \) looks like.

1. The function \( f(x) = (x + 3)^2 \) is a parabola that opens upwards with its vertex at the point \((-3, 0)\).

Next, since we want the graph of \( y = -f(x) \):

2. The graph of \( y = -f(x) \) means that we will reflect the graph of \( f(x) \) across the x-axis. This will turn the upward-opening parabola into a downward-opening parabola.

3. The vertex of \( y = -f(x) \) will remain at the same x-coordinate but will have its y-coordinate inverted. Therefore, the vertex for \( y = -f(x) \) will be \((-3, 0)\), and the parabola will open downwards.

Now, look for the graph that represents the downward-opening parabola with its vertex at \((-3, 0)\).

Since I cannot see the options provided, you would need to identify which of the options is a downward-opening parabola with the vertex at \((-3, 0)\). Look for a graph that matches this description, and that will be the graph of \( y = -f(x) \).