Question

The graph of a quadratic function f(x) has a vertex at (6, -1). What is the vertex of h(x) if h(x) = f(x-3) -4?

Answer 1

(9, -5)

Explanation:

To find the vertex of the function h(x), we need to apply the given transformation to the vertex of the original function f(x).

The function h(x) = f(x - 3) - 4 represents a horizontal shift of 3 units to the right and a vertical shift of 4 units downward from the original function f(x).

Given that the vertex of f(x) is (6, -1), we can apply the horizontal shift of 3 units to the right by adding 3 to the x-coordinate of the vertex, resulting in (6 + 3, -1) = (9, -1).

Next, we apply the vertical shift of 4 units downward by subtracting 4 from the y-coordinate of the vertex, giving us (9, -1 - 4) = (9, -5).

Therefore, the vertex of the function h(x) is (9, -5).