Answer:
g(x) = -x^2
Step-by-step explanation:
The vertex of the original function is (0, 0). Reflection across the x-axis does not change that, but it does change the sign of the vertical scale factor (a).
In vertex form, a quadratic is ...
f(x) = a(x -h)^2 +k . . . . . . . . for vertical scale factor "a" and vertex (h, k)
Since the vertex is (0, 0) and the scale factor is -1 (after reflection), the raw vertex form is ...
g(x) = -1(x -0)^2 +0
Simplifying a bit, we have ...
g(x) = -x^2
