What are the coordinates of the minimum point that relates to the quadratic function f(x)=1/2(x−11)^2+4

Question

Responses

(11, 4)

(4, 11)

(-11, 4)

(11, -4)

Answer 1

To find the coordinates of the minimum point of the quadratic function \( f(x) = \frac{1}{2}(x - 11)^2 + 4 \), we can analyze the function.

This function is in vertex form, \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola. Here, \( a = \frac{1}{2} \) (which is positive, indicating a minimum point), \( h = 11 \), and \( k = 4 \).

Thus, the vertex (minimum point) of the function is at the coordinates \((h, k) = (11, 4)\).

Therefore, the answer is:

\((11, 4)\)