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

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).