Find the zeros of the quadratic function using the square root method. What are the \( x \)-intercepts of the graph of the function? \( g(x)=(x-4)^{2}-25 \) Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A. The zeros and the \( x \)-intercepts are different. The zeros are B. The zeros and the the x-intercepts are .

To find the zeros of the quadratic function \( g(x) = (x - 4)^2 - 25 \), we can first set the function equal to zero: \[ (x - 4)^2 - 25 = 0 \] Next, add 25 to both sides: \[ (x - 4)^2 = 25 \] Now, we take the square root of both sides: \[ x - 4 = \pm 5 \] This gives us two equations to solve: 1. \( x - 4 = 5 \) leads to \( x = 9 \) 2. \( x - 4 = -5 \) leads to \( x = -1 \) Thus, the zeros of the function, which are also the \( x \)-intercepts of the graph, are \( x = 9 \) and \( x = -1 \). B. The zeros and the x-intercepts are 9, -1.