Parabola Properties: Analyzing Negative Values with Downward-Facing Curves and Vertex Position

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

• Step 1: Understand the form of the parabola.
• Step 2: Analyze the nature of values above and below the x-axis.
• Step 3: Determine if the parabola can have positive values.

Now, let's work through each step:

Step 1: Given the parabola is opening downwards, the quadratic formula can be defined as:
$y = a(x-h)^2 + k$, with $a < 0$ and $k > 0$.

Step 2: Because the vertex is above the x-axis ($k > 0$), the vertex itself is positive when considered as a point ($h, k$).

Step 3: A parabola that opens downward will eventually intersect the x-axis, creating two roots unless it remains above the x-axis—which is not generally the case when $k$ is small enough. Therefore, for values of $x$ surrounding the vertex and large enough in magnitude, $y$ can be negative.

Conclusion: The parabola is not always negative as it can be positive near its vertex.

The statement in the problem is thus Incorrect.