which values for h and k are used to write the function f(x) = x² + 12x + 6 in vertex form?\n○ h = 6, k =…

Explanation:

Step1: Recall vertex - form formula

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

For the expression $x^{2}+12x$, we know that $(x + m)^{2}=x^{2}+2mx+m^{2}$. In $x^{2}+12x$, if $2m = 12$, then $m = 6$, and $x^{2}+12x=(x + 6)^{2}-36$. So $f(x)=x^{2}+12x + 6=(x + 6)^{2}-36+6$.

Step3: Simplify the function

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

Answer:

D. $h = - 6,k=-30$