For the function f (x) = 3 (x - 1) 2 + 2, identify the vertex, domain, and range. The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2. The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2. The vertex is (-1, 2), the domain is all real numbers, and the range is y ≥ 2. The vertex is (-1, 2), the domain is all real numbers, and the range is y ≤ 2.

The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2

Step-by-step explanation:

The functions given to us is:

f (x) = 3 (x - 1) ² + 2

Domain:

As there is no limitation of x, all value of x are possible. So

Domain = All real numbers

Range:

For all values of x, the minimum value of y is 2 calculated at x = 1. The rest of the values are greater than 2. So,

Range = y ≥ 2

Vertex:

Simplifying the function:

f (x) = 3 (x² + 1² - 2 (x) (1)) + 2

f (x) = 3 (x² - 2x + 1) + 2

f (x) = 3x² - 6x + 3 + 2

f (x) = 3x² - 6x + 5 (ax² + bx + c)

where a = 3, b = - 6, c = 5

x-coordinate of Vertex is given as:

Vertex (x) = - b/2a = 6/2 (3)

Vertex (x) = 1

Substitute x=1 in the function, we get

Vertex (y) = 2

So Vertex is at (1,2)