Find the domain and range of y=x^(2)+8x+17.

The domain is all real values of x.
This is the equation of a parabola which opens upwards and has a minimum value . To find this minimum value we need to convert to vertex form.

x^2 + 8x + 17 
= (x + 4)^2 - 16 + 17
= (x + 4)^2 + 1

Minimum value is  1

Range is   y >= 1  or   [1, ∞) in interval form.