Question

Complete the square to determine the maximum or minimum value of the function defined by the expression.

x2 + 8x + 6
A) minimum value at 8
B) maximum value at 10
C) minimum value at −14
D) minimum value at −10

Answer 1

Explanation:

Please use the symbol " ^ " to indicate exponentiation: f(x) = x^2 + 8x + 6.

Rewrite this with additional space between the 8x and 6 terms:

x2 + 8x + 6

Take half of the coefficient of x, which is half of 8, or 4.

Square this result: square 4, obtaining 16.

In the space between the 8x and 6 terms, write in + 16 - 16:

x^2 + 8x + 16 -16 + 6

Rewrite x^2 + 8x + 16 as the square of a binomial:

(x + 4)^2 - 10

Comparing this to the standard vertex equation of a quadratic,

(x - h)^2 + k, we see that h must equal -4 and that k must equal -10.

Thus, the vertex of this parabola is (-4, -10), and the minimum value of the function is +10.

Weren't there two more possible answers? If so, please share all of the possible answers. Thank you.