Given f(x) = x^2 - 10x + 22, what is the range of f?

The range is all the possible y-values.

For a parabola that opens up, it is everything greater than the vertex.

If the vertex is (h,k) then the range is y >= k.

Vertex can be found using completing the square:

(h,k) = (5,-3)    ------> Range is y >= -3

Vertex may also be found using formula 
a = 1, b = -10, c = 22


------> Range is y >= -3