Answer:
The vertex of the function is (1 , 2)
The domain is (-∞ , ∞) OR {x : x ∈ R}
The range is [2 , ∞) OR {y : y ≥ 2}
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}