The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function?

A shift 4 units right replaces x with x − 4, and a shift 16 units up adds 16: the new function is f(x − 4) + 16. This gives (x − 4)² + 22(x − 4) + 74 = x² + 14x + 2. Completing the square, x² + 14x + 2 = (x + 7)² − 47, so the vertex form is choice C, (x + 7)² − 47.

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