Question

The graph shows g(x), which is a translation of f(x)=x2. Write the function rule for g(x).

The arch on graph went down to -7 on the y axis

Answer 1

If the parabola's vertex is at (0, −7) (the graph goes down to −7 on the y‑axis), that's f(x)=x^2 shifted down 7 units. So

g(x) = x^2 − 7.

Check: g(0) = −7, as shown.