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

Question

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Answer 1

The function you provided is a quadratic function in vertex form, given by:

\[ f(x) = \frac{1}{2}(x - 11)^2 + 4. \]

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.

From your function, we can identify:

• \( h = 11 \)
• \( k = 4 \)

Since the coefficient \( \frac{1}{2} \) is positive, the parabola opens upwards, meaning that the vertex represents the minimum point of the function.

Thus, the coordinates of the minimum point are:

\[ (11, 4). \]

So, the answer is:

(11, 4)