$\square$ f of $x$ equals, negative 500, $x$ squared, plus $25,000 x$ The revenue $f(x)$, in dollars, that a company receives from sales of a product is given by the function $f$ above, where $x$ is the unit price, in dollars, of the product. The graph of $y=f(x)$ in the $x y$-plane intersects the $x$-axis at 0 and $a$. What does $a$ represent? A. The revenue, in dollars, when the unit price of the product is $\$ 0$ B. The unit price, in dollars, of the product that will result in maximum revenue C. The unit price, in dollars, of the product that will result in a revenue of $\$ 0$ D. The maximum revenue, in dollars, that the company can make
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Answer

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Step 1:
: Identify the given function and its intercepts

The x-axis intercepts can be found by setting $f(x) = 0$ and solving for $x$.

Step 2:
: Solve for the x-axis intercepts

So, the graph intersects the x-axis at $x = 0$ and $
\begin{align*} f(x) &= 0 \ - 500x^2 + 25000x &= 0 \ \end{align*} x = 50$.

Step 3:
: Understand the meaning of the x-axis intercepts

The x-axis intercepts represent the unit prices at which the company receives no revenue. This is because the number of items sold at these prices would be zero (assuming the company doesn't give away the product for free).

Step 4:
: Answer the question

Therefore, the correct answer is option C: The unit price, in dollars, of the product that will result in a revenue of $\$ 0$.

Final Answer

Therefore, the correct answer is option C: The unit price, in dollars, of the product that will result in a revenue of $\$ 1$.