Question

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

Answer 1

The the vertex is: (2, 4)

Domain: all real numbers

Range:
`[4 \infty)`

Explanation:

Quadratic functions can be written vertically as follows

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

Quadratic functions can be written vertically as follows

Where the point (h, k) represents the vertex of the quadratic function.

For this type of functions the domain is always all real numbers and the range is
`[k, \infty)` or if
`a <0` then the range is
`(-\infty, k]`

In this case the function is:

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

So

`h = 2\\k=4`

The the vertex is: (2, 4)

Domain: all real numbers

Range:
`[4, \infty)`