Determining x-Values for Positive Parabola Behavior between Points A and B

To solve this problem, we need to determine where the function $f(x)$ is positive. The graph of the parabola intersects the $x$-axis at points $A$ and $B$, indicating these are the roots of the function.

The behavior of the function depends on the direction in which the parabola opens:

• If the parabola opens upwards ($a > 0$), the function is positive between the roots, that is in the interval $(A, B)$.
• Conversely, if the parabola opens downwards ($a < 0$), the function is positive outside of the roots.

In the problem, although the nature (upwards or downwards opening) is not explicitly stated, the most common interpretation for an intersection analysis suggests that the parabola opens upwards ($a > 0$). Thus, the values of $x$ where $f(x) > 0$ are precisely those between the roots $A$ and $B$.

Therefore, the solution to the problem is $A < x < B$.