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Nonlinear functions SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

$f of x equals, negative 500, x squared, plus 25,000 x$

The revenue $f of x$ , 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 $y equals f of x$ in the xy-plane intersects the x-axis at 0 and a. What does a represent?

ExplanationShow

Choice C is correct. By definition, the y-value when a function intersects the x-axis is 0. It’s given that the graph of the function intersects the x-axis at 0 and a, that x is the unit price, in dollars, of a product, and that $f of x$ , where $y equals f of x$ , is the revenue, in dollars, that a company receives from the sales of the product. Since the value of a occurs when $y equals 0$ , a is the unit price, in dollars, of the product that will result in a revenue of $0.

Choice A is incorrect. The revenue, in dollars, when the unit price of the product is $0 is represented by $f of x$ , when $x equals 0$ . Choice B is incorrect. The unit price, in dollars, of the product that will result in maximum revenue is represented by the x-coordinate of the maximum of f. Choice D is incorrect. The maximum revenue, in dollars, that the company can make is represented by the y-coordinate of the maximum of f.

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Nonlinear functions SAT question

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