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.

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 
.

GPT-4o mini · Answer

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) $.