Parabola Property: Analyzing Positive Values with X-Axis Vertex

To solve this problem, follow these steps:

• Step 1: Recognize that the standard form of a quadratic function is $f(x) = a(x - h)^2 + k$, which represents a parabola.
• Step 2: Since the parabola is upward-opening, the coefficient $a$ is positive, $a > 0$.
• Step 3: Given that the vertex is on the x-axis, the vertex has coordinates $(h, 0)$, which means $k = 0$.
• Step 4: Substitute $k = 0$ into the standard form to get $f(x) = a(x - h)^2$.
• Step 5: Since $a > 0$, the expression $a(x - h)^2$ is always non-negative because $(x - h)^2 \geq 0$ for all $x$.
• Step 6: At the vertex $x = h$, $f(h) = a(h - h)^2 = 0$; at any other point, $f(x) > 0$ since $a(x - h)^2 > 0$.

Therefore, the function value is zero at the vertex and positive everywhere else. This confirms that the statement is correct.

The correct answer to the problem is Correct.