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Question: An ornithologist tracks a bird’s migration path, which follows the quadratic equation $ y = -x^2 + 6x - 8 $. Determine the maximum height $ y $ reached during the flight.
Solution: The maximum height occurs at the vertex. For $ y = -x^2 + 6x - 8 $, $ a = -1 $, $ b = 6 $, so $ x = -\frac{6}{2(-1)} = 3 $. Substitute $ x = 3 $: $ y = -(3)^2 + 6(3) - 8 = -9 + 18 - 8 = 1 $. The maximum height is $ 1 $ unit. \boxed{1}
Question: Given $ f(2x + 1) = 4x^2 + 12x + 9 $, find $ f(x^2 - 3) $.

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