Solve f(x) > 0 on the Graph: Finding Specific x Values

To solve the given problem using the graph, we need to determine the intervals along the x-axis where the quadratic function $f(x)$ is positive, based on its x-intercepts $x = -11$ and $x = -1$ as shown on the graph.

• Step 1: Identify the x-intercepts from the graph: $x = -11$ and $x = -1$.
• Step 2: Interpret the graph of the quadratic function. Since it is a parabola opening upwards and touches the x-axis at $x = -11$ and $x = -1$, these are points where the quadratic changes sign.
• Step 3: Determine the intervals: The graph is above the x-axis (positive) between the x-intercepts because the parabola is opening upwards. Therefore, the function is positive for $-11 < x < -1$.

The conclusion is that the quadratic function $f(x)$ is greater than zero in the interval $-11 < x < -1$.

Therefore, the correct answer is $\mathbf{-11 < x < -1}$.