Answer:

1To determine the smallest value of f(x) we need to find the vertex of the parabola. We can do this by completing the square:

f(x) = x² +8x+21

f(x) = (x+4)² - 3

The vertex is at (-4,-3) and the smallest value of f(x) is -3.

2Again, we need to complete the square to find the vertex:

f(x) = x² +10x+13

f(x) = (x+5)² - 12

The vertex is at (-5,-12) and the smallest value of f(x) is -12.