Parabola Properties: Analyzing Negative Values with Downward-Facing Vertex Below X-axis

The problem concerns a downward-opening parabola with a vertex below the x-axis. Let's elaborate on these terms to determine if the given statement is correct:

• Step 1: Identify Quadratic Form
  We consider a quadratic function $f(x) = ax^2 + bx + c$ with $a < 0$ since it opens downwards.
• Step 2: Understand the Vertex's Position
  The vertex form of the quadratic is $f(x) = a(x - h)^2 + k$. Given that the vertex is below the x-axis, the condition $k < 0$ holds. The vertex at coordinate $(h, k)$ is the maximum point of the parabola.
• Step 3: Evaluate the Parabola's Sign
  Since $k < 0$, the vertex $(h, k)$ is the highest point of the parabola lying below the x-axis. Consequently, all other points on the parabola satisfy $f(x) \leq k < 0$.

Therefore, the entire quadratic function is negative for all values of $x$ due to the vertex being the maximum and its y-coordinate being negative. Thus, the statement that such a parabola is always negative is indeed "correct".

Thus, the correct choice is: $\text{Correct}$.