Question

The parent function of the function g(x) = (x - 1)^2 + k is f(x) = x^2. The vertex of the function g(x) is located at (9, -8). What are the values of h and k?

a) h = 9, k = -8
b) h = 1, k = -8
c) h = -1, k = 8
d) h = -9, k = 8

Answer 1

The values of h and k in the function g(x) = (x - 1)^2 + k with a vertex at (9, -8) are h = 8 and k = -8.Therefore, the values of h and k are h = 8 and k = -8.

Step-by-step explanation:

The parent function of the function g(x) = (x - 1)^2 + k is f(x) = x^2.

The vertex of the function g(x) is located at (9, -8).

To find the values of h and k, we need to match the vertex of g(x) to the parent function f(x).

Since the vertex of g(x) is (9, -8), we can equate the x-coordinate of the vertex to h + 1 and the y-coordinate of the vertex to k.

So, we have:

h + 1 = 9

k = -8

From the first equation, we can solve for h: h = 9 - 1 = 8.

Therefore, the values of h and k are h = 8 and k = -8.