Finding X: Positive Values of a Parabola Intersection Problem

The graph of the parabola intersects the X-axis at points A and B. This tells us these are the roots of the quadratic equation, and that $f(x) = 0$ at these points. Given that the shape of the parabola (concave up or down) affects where it is positive or negative:

From the graph:

• If the parabola opens upwards (which it must, if we are finding $f(x) > 0$ outside A and B), it is positive when $x \lt A$ or $x \gt B$, as the parabola dips below the X-axis between A and B.
• If the parabola opens downwards, it would be positive between A and B, however, our task is to identify the actual nature based on a graphical interpretation.

The graph signifies the function is positive outside the interval $A \lt x \lt B$.

Therefore, the intervals where $f(x) > 0$ are:

$x > B$ or $x < A$

The answer choice that corresponds to this interpretation is:

$x > B$ or $x < A$