Analyzing Function Graphs: Determine Positive X Intervals for f(x)

To solve this problem effectively, follow these steps:

• Step 1: Identify where the parabola crosses the x-axis. These are the x-intercepts or roots. Let’s call these intercepts $x_1$ and $x_2$.
• Step 2: Since the question asks for $f(x) > 0$, we need to find where the graph is above the x-axis.
• Step 3: Examine the sketch: The parabola dips below the x-axis after the first root and re-emerges above it until the second root, which is characteristic of a quadratic function.
• Step 4: Thus, the function is positive between the two intercepts.

From the sketch, it is clear that the x-values where the function $f(x) > 0$ are between the two intercepts, specifically $(x_1, x_2)$, which look like $2$ and $8$ on the graph.

Therefore, for this problem, the interval where $f(x) > 0$ is $2 < x < 8$.

The solution to this problem is $2 < x < 8$.