Question

find the decreasing interval
x>2
x>-2
x<-2
x<2

Explanation:

Step1: Analyze the graph of the quadratic function

For a quadratic function \(y = ax^{2}+bx + c\) (\(a>0\)), its graph is a parabola opening upwards. The function is decreasing on the left side of the axis of symmetry and increasing on the right side of the axis of symmetry.

Step2: Find the axis of symmetry

The axis of symmetry of the quadratic function \(y = ax^{2}+bx + c\) is \(x=-\frac{b}{2a}\). From the graph, we can observe that the axis of symmetry \(x = - 2\).

Step3: Determine the decreasing interval

Since the parabola opens upwards (\(a>0\)), the function is decreasing when \(x < - 2\).

Answer:

\(x < - 2\)