A company models its profit and cost functions as P⁡(x)=−4⁢x^2+16⁢x−10 and C⁡(x)=2⁢x^2−8⁢x+15 What can be inferred about the nature of these functions based on the direction in which their parabolas open?

For a quadratic function, the sign of the x² coefficient determines the direction its parabola opens. In P(x), the coefficient is −4, so its parabola opens downward; in C(x), the coefficient is 2, so its parabola opens upward. Thus P(x) represents a profit function and C(x) a cost function, matching choice C.

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