Finding Negative Values of a Parabolic Function with Vertex on X-axis

To solve this problem, we need to determine when $f(x)$ is negative by analyzing the graph provided.

The graph shows a quadratic function shaped as a parabola. Importantly, the parabola intersects the x-axis precisely at point A, which is its vertex. From this, we can deduce two possible scenarios:

1. If the parabola opens upwards (convex), the vertex represents the minimum point. Thus, the y-value at the vertex is greater than any other point on the function, implying there is no region where $f(x) < 0$ since the lowest point is zero.

2. If it were to open downwards, point A would be the maximum, and $f(x)$ could be negative elsewhere, but this contradicts the given information that point A is a vertex on the x-axis, suggesting the opening is upwards.

Since the graph passes through the x-axis only at vertex A and that is the minimum point, the parabola opens upwards. Therefore, the function $f(x)$ never takes negative values as it only touches the x-axis without crossing it.

Thus, the conclusion is that there are no values of $x$ for which $f(x) < 0$.

Hence, the function has no negative domain.