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

Question

?(1 point)

Answer 1

The given quadratic function is

$$f(x)=12(x-11{)}^2+4.$$

To find the minimum point of this function, we can analyze its structure. This is a parabola that opens upwards (since the coefficient of the squared term is positive, $12$). The vertex of a parabola in the form $f(x)=a(x-h{)}^2+k$ is at the point $(h,k)$.

In your function, $h=11$ and $k=4$. Therefore, the coordinates of the minimum point (the vertex) are

$$(11,4).$$

Now, if you are asking about the square root function that relates to $f(x)$, this function, since it is a quadratic function, has a minimum point at $(11,4)$ and does not require any additional transformation via a square root function.

Thus, the minimum point for the function $f(x)$ you provided is

$$\boxed{{\displaystyle (11,4)}}.$$