For the function f(x) = 3(x - 1)2 + 2, identify the vertex, domain, and range.
Solution:
Given, the function is f(x) = 3(x - 1)2 + 2
We have to find the vertex, domain and range for the given function.
The vertex form of a quadratic function is given by
\(f(x)=(x-h)^{2}+k\)
Where, (h, k) is the vertex of the function.
The given function represents a vertical parabola open up, so the vertex is minimum.
From the function,
h = 1, k = 2
Therefore, the vertex is the point (1, 2)
The domain is all real numbers in the interval \((-\infty,\infty )\)
The range is f(x) >= 2
Range lies in the interval \((2,\infty )\)
Therefore, the vertex, domain and range is (1, 2), \((-\infty,\infty )\) and \((2,\infty )\).
For the function f(x) = 3(x - 1)2 + 2, identify the vertex, domain, and range.
Summary:
For the function f(x) = 3(x - 1)2 + 2, vertex is (1, 2), domain is all the real numbers in the interval \((-\infty,\infty )\), range lies in the interval \((2,\infty )\)