A company’s profit is modeled by the quadratic function with zeros 6 and 42 The point open paren 15 comma 81 close paren also lies on the boundary line. Any values above the boundary line exceed the expected profits. What is the standard form of the quadratic inequality represented by the description?

Since the zeros are 6 and 42, the boundary can be written as y = a(x − 6)(x − 42). Substituting the point (15, 81) gives 81 = a(9)(−27), so a = −1/3. Expanding gives y = −1/3x² + 16x − 84. Values above the boundary have greater y-values, so the inequality is y > −1/3x² + 16x − 84, choice C.

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