For the function f(x)=3(x-1)^2+2 identify the vertex, domain, and range.

The vertex of the function is (1 , 2)

The domain is (-∞ , ∞) OR {x : x ∈ R}

The range is [2 , ∞) OR {y : y ≥ 2}

Step-by-step explanation:

* Lets revise the standard form of the quadratic function

- The standard form of the quadratic function is

  f(x) = a(x - h)² + k , where (h , k) is the vertex point

- The domain is the values of x which make the function defined

- The domain of the quadratic function is x ∈ R , where R is the set

 of real numbers

- The range is the set of values that corresponding with the domain

- The range of the quadratic function is y ≥ k if the parabola upward

  and y ≤ k is the parabola is down ward

* Lets solve the problem

∵ f(x) = 3(x - 1)² + 2

∵ f(x) = a(x - h)² + k

∴ a = 3 , h = 1 , k = 2

∵ The vertex of the function is (h , k)

∴ The vertex of the function is (1 , 2)

- The domain is all the real number

∵ The domain of the quadratic function is x ∈ R

∴ The domain is (-∞ , ∞) OR {x : x ∈ R}

- The leading  coefficient of the function is a

∵ a = 3 ⇒ positive value

∴ The parabola is opens upward

∴ The range of the function is y ≥ k

∵ The value of k is 2

∴ The range is [2 , ∞) OR {y : y ≥ 2}

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

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