Parabola Analysis: Finding Positive Values Where f(x) > 0 at Vertex Point

To identify the conditions where f(x) > 0 , we need to analyze the nature of the quadratic function as represented on the provided graph.

Based on the problem, the graph intersects the x-axis exactly at one point, recognized as point A, the vertex. In a quadratic function $ax^2 + bx + c$, if the vertex intersects at the x-axis and nowhere else, it means the graph is tangent to the x-axis at that vertex.

To determine if the function is positive, examine the orientation: - If a > 0 , the parabola opens upwards, making it have a minimum at the vertex. - If a < 0 , the parabola opens downwards, making it have a maximum at the vertex. Given that the problem states the parabola intersects the x-axis only at the vertex, the parabola opens downward. This is inferred from the phrased graph where no areas reach above the x-axis.

Therefore, the function never reaches a value greater than zero, as the parabola is concave down, and the vertex sits on the x-axis.

Conclusively, the range where f(x) > 0 is nonexistent given the parameters of the problem.

Therefore, the solution is that there are no such values.