which values for h and k are used to write the function f(x) = x² + 12x + 6 in vertex form?\no h=6, k=36\no…

Explanation:

Step1: Recall vertex - form of a quadratic function

The vertex - form of a quadratic function is (y=a(x - h)^2+k), and for the quadratic function (y = ax^{2}+bx + c), we can complete the square. Given (f(x)=x^{2}+12x + 6), where (a = 1), (b = 12), (c = 6).

Step2: Complete the square for the (x) - terms

First, take the coefficient of (x), which is (b = 12). Half of it is (\frac{b}{2}=\frac{12}{2}=6), and then square it: ((\frac{b}{2})^2=36). We rewrite (f(x)) as (f(x)=x^{2}+12x+36-36 + 6).

Step3: Factor the perfect - square trinomial

(x^{2}+12x + 36=(x + 6)^2), so (f(x)=(x + 6)^2-30). Comparing with the vertex - form (y=a(x - h)^2+k), we have (h=-6) and (k=-30).

Answer:

D. (h = - 6,k=-30)