Complete the square to determine the maximum or minimum value of the function defined by the expression. x2 + 8x + 6

Minimum at (-4, - 10)

Step-by-step 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).