Question

For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.

Answer 1

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. Hence, for the given function, vertex = (2, 4)
Domain is all real numbers and range is {f(x) : f(x) >= 4}

Answer 2

we have

`f(x) = (x - 2)^(2) + 4`

This is a vertical parabola open up, so the vertex is a minimum

we know that

The vertex form of a vertical parabola function is given by the formula

`f(x) = (x - h)^2 + k`

where

(h, k)----------> is the vertex of the function

In this problem

the vertex is the point (2,4)

The domain is all real numbers----------> interval (-∞,∞)

The range is the interval------------> [4, ∞)

using a graph tool

see the attached figure