Question

where is the graph decreasing? -\infty < x < 3 -\infty < x < -1 3 < x < \infty -1 < x < \infty

Explanation:

Step1: Understand the concept of a decreasing graph

A graph is decreasing when, as \(x\) increases, \(y\) decreases. For a parabola \(y = ax^{2}+bx + c\) (\(a>0\) opens upwards), it decreases to the left of the vertex.

Step2: Locate the vertex of the parabola

From the graph, the vertex (the minimum point of the upward - opening parabola) has an \(x\) - coordinate of \(x=-1\).

Step3: Determine the interval of decrease

Since the parabola opens upwards (\(a > 0\)), the function is decreasing for \(x\) values less than the \(x\) - coordinate of the vertex. So the interval where the graph is decreasing is \(-\infty

Answer:

B. \(-\infty < x < - 1\)