Question

The function `f(x)=x^{2}` was transformed to create the function `g(x)=f(x-3)-4`. What are the coordinates of the vertex of the graph `g`?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the vertex of the graph of `g(x)=f(x-3)-4`, we first need to determine the vertex of the original function `f(x)=x^2` and then perform the transformation.

The vertex of the function `f(x)=x^2` is at (0,0) since the function is in the form `f(x) = a(x-h)^2 + k`, where (h, k) is the vertex. In this case, h=0 and k=0.

To transform the function to `g(x)=f(x-3)-4`, we need to shift the vertex of `f(x)` 3 units to the right and 4 units downwards. So, the new vertex will be at (3,-4).

Therefore, the coordinates of the vertex of the graph `g` are (3,-4).