What is the range of the function #f(x)=x^2+2x+2#?
The function can be rewritten as
Thus, the range is
Since this is an upward facing parabola, we know that the upper bound of the range is
Find the minimum. We can do this by either using our knowledge of parabolas and quadratic form to complete the square to find the vertex, and the y value is the minimum; OR we could use calculus and find where
Vertex is at
The minimum is at