What is the domain and range of

f (x) = 2x^2+6x+2

As is the case for any polynomial, the domain of this one is (-infinity, + infinity).

To find the range, we need to determine the minimum value that f (x) can have. The coefficients here are a=2, b=6 and c = 2,

The x-coordinate of the vertex is x = - b / (2a), which here is x = - 6/4 = - 3/2.

Evaluate the function at x = 3/2 to find the y-coordinate of the vertex, which is also the smallest value the function can take on. That happens to be y = - 5/2, so the range is [-5/2, infinity).