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.