Answer:
Minimum at (-4, -10)
Explanation:
x² + 8x + 6
The coefficient of x² is positive, so the parabola opens upward, and the vertex is a minimum.
Subtract the constant from each side
x² + 8x = -6
Square half the coefficient of x
(8/2)² = 4² = 16
Add it to each side of the equation
x² + 8x + 16 = 10
Write the left-hand side as the square of a binomial
(x + 4)² = 10
Subtract 10 from each side of the equation
(x+ 4)² -10 = 0
This is the vertex form of the parabola:
(x - h)² + k = 0,
where (h, k) is the vertex.
h = -4 and k = -10, so the vertex is at (-4, -10).
The Figure below shows your parabola with a minimum at (-4, -10).