Question

Find the range of the function.

f(x) = (x - 2)2 + 2


a. All real numbers
b. y ≥ 0
c. y > 2
d. y ≥ 2

Answer 1

The vertex form of a quadratic function is given by

`f(x)=a (x-h)^(2) +k`, where (h, k) is the vertex of the equation.
In the given function, (h, k) = (2, 2), also a = 1 which is positive, this means that the parabola is facing up, hence the range is given by y ≥ k.
Therefore, range is y ≥ 2.