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

To find the vertex of the graph g, we first need to find the vertex of the original function f(x) = x^2, which is at (0, 0).

Next, we apply the transformations to the vertex of f(x) to find the vertex of g(x) = f(x - 3) - 4.

Since the function f(x) = x^2 has its vertex at (0, 0), the transformation f(x - 3) will shift the graph to the right by 3 units, so the new x-coordinate of the vertex will be 3.

Then, the transformation f(x - 3) - 4 will shift the graph downward by 4 units, so the new y-coordinate of the vertex will be -4.

Therefore, the vertex of the graph g is (3, -4).