Consider the quadratic functions C⁡(x)=3⁢x^2−12⁢x+7 and R⁡(x)=−2⁢x^2+8⁢x−3 Which statement correctly identifies the nature of each function based on the direction of their parabolas?

For a quadratic function, the sign of the x² coefficient determines the direction its parabola opens. C(x) has coefficient 3, which is positive, so it opens upward and represents a cost function. R(x) has coefficient −2, which is negative, so it opens downward and represents a profit function. Therefore, the correct statement is D.

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