Parabola Property: Analyzing Negative Values for X-Axis Vertex Functions

To solve this problem, let's analyze the given conditions:

• Step 1: We examine the standard form of a downward-opening parabola. The standard vertex form is $y = a(x - h)^2 + k$. If the vertex lies on the x-axis, $k = 0$, so the equation simplifies to $y = a(x - h)^2$.
• Step 2: Since the parabola is bending downwards, it implies that $a < 0$. Therefore, the quadratic term $a(x - h)^2$ is non-positive for all values of $x$, becoming 0 only when $x = h$.
• Step 3: Evaluate the function for $x \neq h$. For any $x \neq h$, $(x - h)^2 > 0$, so $y = a(x - h)^2 < 0$ because $a < 0$.

Conclusively, the function value is always negative for all $x \neq h$, and it is exactly zero at $x = h$ (the vertex). The statement provided corresponds precisely with this behavior.

Therefore, the statement that the function is always negative except at the vertex point is indeed Correct.