An $x$-intercept is a point where the graph crosses the $x$-axis, meaning $y = f(x) = 0$. The problem states that the graph intersects the $x$-axis at $0$ and $a$, which correspond to the ordered pairs $(0, 0)$ and $(a, 0)$.

At the point $(a, 0)$:

• The first coordinate, $x = a$, represents a unit price (in dollars).
• The second coordinate, $y = 0$, represents a revenue of $0.

Therefore, $a$ represents the unit price, in dollars, of the product that will result in a revenue of $0.

Step 3: Evaluate the Choices

• A: Incorrect. That would be the $y$-value when $x = 0$, which is $f(0) = 0$.
• B: Incorrect. The price that maximizes revenue is the $x$-coordinate of the vertex ($x = 25$), not the $x$-intercept.
• C: Correct. $a$ is a unit price that produces $f(a) = 0$ dollars of revenue.
• D: Incorrect. The maximum revenue is the $y$-coordinate of the vertex ($f(25) = 312,500$).