A quadratic inequality contains the values less than or equal to the quadratic function that has a vertex of open paren negative 9 comma negative 27 close paren and contains the point open paren 1 comma 39 and 2 thirds close paren on the boundary. Which inequality in vertex form represents the description?

Vertex form is y = a(x − h)² + k. With vertex (−9, −27), this becomes y = a(x + 9)² − 27. Substituting the boundary point (1, 39⅔) gives 39⅔ = 100a − 27, so 100a = 66⅔ and a = ⅔. Since the inequality includes values less than or equal to the function, the answer is C: y ≤ ⅔(x + 9)² − 27.

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