Question

The function f(x)=x2 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

Thanks! That's Correct!

Answer 2

To find the vertex of the graph of g(x), we will first need to find the vertex of the graph of f(x)=x^2.

The vertex of a parabola of the form f(x) = ax^2 + bx + c is given by the point (h, k), where h = -b/(2a) and k = f(h). In this case, a = 1, b = 0, and c = 0, so the vertex of the graph of f(x) = x^2 is at the point (0, 0).

Now, to find the vertex of the graph of g(x) = f(x-3) - 4, we will need to shift the vertex of the graph of f(x) = x^2 three units to the right and four units downward.

Since the vertex of the graph of f(x) is at (0, 0), the vertex of the graph of g(x) will be at (3, -4).

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

Answer 3

You're welcome! If you have any more questions or need further clarification, feel free to ask!