# For the function f(x) = (x - 2)^{2} + 4, identify the vertex, domain, and range.

**Solution:**

Given, the function is f(x) = (x - 2)^{2} + 4

We have to find the vertex, domain and range for the given function.

The vertex form of a quadratic function is given by

\(f(x)=(x-h)^{2}+k\)

Where, (h, k) is the vertex of the function.

The given function represents a vertical parabola open up, so the vertex is minimum.

From the function,

h = 2

k = 4

Therefore, the vertex is the point (2, 4)

The domain is all real numbers in the interval \((-\infty,\infty )\)

The range is f(x) >= 4

Therefore, the range lies in the interval \((4,\infty )\)

## For the function f(x) = (x - 2)^{2} + 4, identify the vertex, domain, and range.

**Summary:**

For the function f(x) = (x - 2)^{2} + 4, vertex is (2, 4), domain is all the real numbers in the interval \((-\infty,\infty )\), range lies in the interval \((4,\infty )\)

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