Which inequality in vertex form represents the region less than the quadratic function with vertex (–2, 2) and includes the point (–4, 14) on the boundary?

Vertex form is y = a(x − h)² + k. With vertex (−2, 2), the function is y = a(x + 2)² + 2. Substitute the boundary point (−4, 14): 14 = a(−4 + 2)² + 2, so 12 = 4a and a = 3. The region below the quadratic uses y <, giving y < 3(x + 2)² + 2, choice A.

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