Parabola Property Analysis: Vertex Position Below X-axis and Positive Values

To analyze this problem, we'll follow these steps:

• Step 1: Understand the structure of a quadratic function.
• Step 2: Explore the implications of the vertex location below the x-axis.
• Step 3: Analyze specific conditions where the function might not be always positive.

Step 1:
A parabola $y = ax^2 + bx + c$ opens upwards if $a > 0$.

Step 2:
The vertex form of a quadratic is $y = a(x-h)^2 + k$, where $(h, k)$ is the vertex. If $k < 0$, the vertex is below the x-axis, making $y$ negative at $x = h$ (the minimum point for an upward-opening parabola).

Step 3:
Since $y$ at the vertex is $k < 0$, it implies the function is negative at least at this point. Thus, the function cannot always be positive, as there exists at least one point where it is non-positive (negative).

Therefore, the assertion that the parabola is always positive is incorrect.

The correct answer is: Incorrect.