Use this to answer the question.

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

(1 point)
The of y=−f(x)
is option
.

Answer 1

To find the graph of \( y = -f(x) \) where \( f(x) = (x + 3)^2 \), we first need to understand the original function and then how the negative transformation affects it.

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

2. Transforming to \( y = -f(x) \): The transformation \( y = -f(x) \) reflects the graph of \( f(x) \) across the x-axis. Thus, the vertex of the new function \( g(x) = -f(x) = -(x + 3)^2 \) will now be at \((-3, 0)\) but will open downward instead of upward.

3. Describing \( y = -f(x) \): The graph of \( y = -f(x) \) will still be a parabola, but it will be inverted, having a vertex at \((-3, 0)\) and opening downward.

Given the information, if we consider labeled options for the graphs to identify which represents \( y = -f(x) \), the correct option will be the one depicting a downward-opening parabola with the vertex at \((-3, 0)\).

Therefore, the answer is: "The graph of \( y = -f(x) \) is option [the option that shows a downward-opening parabola with a vertex at (-3, 0)]."