Question

determine the domain on which the following function is decreasing.
answer attempt 1 out of 2
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Explanation:

Step1: Identify the vertex's x - coordinate

The graph is a parabola opening downwards (since it has a maximum point). The vertex of the parabola is the highest point. From the graph, we can see that the vertex occurs at \(x = 7\) (by looking at the grid, the peak is at \(x = 7\)).

Step2: Determine the interval where the function is decreasing

A function is decreasing when as \(x\) increases, \(y\) decreases. For a downward - opening parabola, the function is decreasing to the right of the vertex. The domain of the function starts from \(x = 0\) (the y - intercept) and ends at \(x = 15\) (the x - intercept). But the decreasing part starts at the vertex's x - coordinate (\(x = 7\)) and goes to the rightmost point of the domain (\(x = 15\)). So the function is decreasing on the interval \([7,15]\) (we use square brackets because the endpoints are included; at \(x = 7\) the function reaches its maximum and then starts to decrease, and at \(x = 15\) the function value is \(0\)).

Answer:

\([7,15]\)