Answer:
-5
Explanation:
You want the minimum value of f(x) = x² +6x +4.
Line of symmetry
The line of symmetry of a quadratic function f(x) = ax² +bx +c is given by ...
x = -b/(2a)
The line of symmetry passes through the extreme point. When a > 0, that extreme point is the minimum.
Here, we have a=1, b=6, so the line of symmetry is ...
x = -6/(2·1) = -3
Extreme
The extreme point (minimum) is ...
f(-3) = (-3)² +6(-3) +4 = (-3 +6)(-3) +4 = -9 +4
f(-3) = -5
The minimum value of f(x) is -5.