Parabola Vertex on X-axis: Analyzing Positive Value Behavior

To determine if a parabola with its vertex on the x-axis is always positive except for the vertex point, consider the vertex form of a quadratic function: $y = a(x-h)^2 + k$

• Since the vertex is on the x-axis, we have $k = 0$, so the equation simplifies to $y = a(x-h)^2$.
• The vertex of the parabola is the point $(h, 0)$.
• If $a > 0$, the parabola opens upwards, meaning $y$ values are always non-negative but equal zero at the vertex.
• If $a < 0$, the parabola opens downwards, indicating the vertex is at a maximum point, and all other $y$ values are negative.
• Therefore, the behavior of the parabola (whether it is always positive except at the vertex) is dependent on the sign of $a$, which is not specified in the problem.

Without knowing the sign of $a$, we cannot definitively determine if the parabola is always positive except at the vertex. Thus, the answer is that the outcome "cannot be determined" from the given information.

Therefore, the correct answer choice is Cannot be determined.