Question

The function g(x) is a translation of f(x) = (x + 3)2 – 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)?

g(x) = (x – 2)2 + k
g(x) = (x + 8)2 + k
g(x) = (x – h)2 – 5
g(x) = (x – h)2 – 15

Answer 1

f(x) = (x + 3)^2 − 10 has axis x = −3. Moving that axis 5 units right gives x = −3 + 5 = 2, so g must be of the form (x − 2)^2 + k. Thus the first option fits; with the same vertical position k = −10 the translated function is g(x) = (x − 2)^2 − 10.