Parabola Intersection Analysis: Find X Where f(x) < 0

To solve this problem, let's analyze the graph of the quadratic function around points A and B where it intersects the $x$-axis.

• Step 1: Identify the nature of the quadratic. From the graph, it is clear that the parabola intersects the $x$-axis, suggesting $f(x) = 0$ at these points.
• Step 2: Since the problem indicates points A and B as interceptions, we can conclude the parabola crosses or touches the $x$-axis at these points.
• Step 3: Determine where $f(x) < 0$. Since A and B are roots, the parabola's graph will be below the $x$-axis between A and B if the parabola opens upwards, given by $A < x < B$. If it opens downwards, the parabola would be negative outside A and B. Based on typical quadratic behavior with a vertex below the $x$-axis, the parabola likely opens upwards.

The solution, therefore, is found within the interval between the intercepts on an upward-opening parabola. This conclusion is consistent with the graphical representation of most standard quadratics.

Thus, the values of $x$ where $f(x) < 0$ are precisely in the interval $A < x < B$.