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?
To find the vertex of the graph of g(x), we first need to find the vertex of the graph of f(x) = x^2.
The vertex of the graph of f(x) = x^2 is at the point (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. The vertex of f(x) = x^2 is at (0, 0).
Now, we need to consider the transformation of f(x) to create g(x) = f(x-3) - 4. The transformation involves shifting the graph of f(x) three units to the right and four units down.
Therefore, the new x-coordinate of the vertex of g(x) will be h + 3 = 0 + 3 = 3, and the new y-coordinate of the vertex will be k - 4 = 0 - 4 = -4.
So, the vertex of the graph of g(x) = f(x-3) - 4 is at the point (3, -4).