Question

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.

Answer 1

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

Explanation:

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Answer 2

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

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)