The function g of x is a translation of f of x is equal to open paren x plus 3 close paren squared minus 10 The axis of symmetry of g of x is 5 units to the right of f of x Which function could be g of x ?

The axis of symmetry of f(x) = (x + 3)² − 10 is x = −3, since the vertex form is (x − h)² + k. Moving 5 units to the right gives an axis of symmetry at x = −3 + 5 = 2. A translated function with that axis has the form g(x) = (x − 2)² + k, so choice C fits.

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