Question

Which function has a vertex at (2, 9)?

a. f(x) = -(x - 3)^2
b. f(x) = (x + 8)^2
c. f(x) = (x - 5)(x + 1)
d. f(x) = -(x - 1)(x - 5)

Answer 1

The function that has a vertex at (2, 9) is option a. f(x) = -(x - 3)^2.

Step-by-step explanation:

The function that has a vertex at (2, 9) is option a. f(x) = -(x - 3)^2.

To find the vertex of a quadratic function in the form f(x) = a(x - h)^2 + k, the vertex is located at the point (h, k). In this case, the vertex is (3, 0).

However, since the function is reflected vertically, the y-coordinate of the vertex is negated, making the vertex (3, -9). Therefore, the correct option is a. f(x) = -(x - 3)^2.