Which is the inequality in factored form that represents the region greater than or equal to the quadratic function with zeros negative 3 point 5 and 11 point 5 and includes the point open paren 8 point 5 comma negative 54 close paren on the boundary?

With zeros at −3.5 and 11.5, the quadratic has factors (x + 3.5)(x − 11.5), so write it as y = a(x + 3.5)(x − 11.5). Substituting the boundary point (8.5, −54) gives −54 = a(12)(−3) = −36a, so a = 3/2. The region is greater than or equal to the quadratic, making the inequality y ≥ 3/2(x + 3.5)(x − 11.5), which is choice D.

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