Question

What are the coordinates of the minimum point for the square root function that relates to the quadratic function f(x)=12(x−11)2+4?

Answer 1

If you take the square root of f(x), you get g(x) = sqrt(12(x−11)^2 + 4). The quadratic f(x) has its vertex at x = 11 with f(11) = 4, and since sqrt is increasing, g(x) is minimized at the same x. Thus the minimum point is (11, 2).

(For reference, the quadratic itself has minimum point (11, 4).)