What is the range of the function $f (x) = {(x - 2)}^{2} + 2$ $f(x) = (x - 2)^2 + 2$ ?

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Answer 1 · 2017-06-27T08:09:22

See explanation.

The graph of this function is a parabola with vertex at $(2, 2)$ $(2,2)$ and the graph is going "upwards" from the vertex (see graph)

graph{x^2-4x+6 [-9.96, 10.04, -0.68, 9.32]}

From this graph you can say that the function's range is $[2; + \infty)$ $[2;+oo)$

What is the range of the function f(x)=(x−2)2+2f(x) = (x - 2)^2 + 2?