Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex (–6, 12) and includes the point (–9, 15) on the boundary?

A quadratic with vertex (−6, 12) has vertex form y = a(x + 6)² + 12. Substitute the boundary point (−9, 15): 15 = a(−9 + 6)² + 12 = 9a + 12, so a = 1/3. Since the region is less than or equal to the function, the inequality is y ≤ ⅓(x + 6)² + 12, choice B.

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