what is the vertex of the function f(x) = x² + 12x?\n(-6, -36)\n(-6, 0)\n(6, 0)\n(6, -36)

Explanation:

Step1: Recall vertex - form of quadratic function

The general form of a quadratic function is $y = ax^{2}+bx + c$, and its vertex - form is $y=a(x - h)^{2}+k$, where the vertex is $(h,k)$. For the function $f(x)=x^{2}+12x$, we have $a = 1$, $b = 12$, and $c = 0$. We can complete the square.

Step2: Complete the square

[ \begin{align*} f(x)&=x^{2}+12x\ &=x^{2}+12x+36 - 36\ &=(x + 6)^{2}-36 \end{align*} ] Comparing with the vertex - form $y=a(x - h)^{2}+k$, we have $h=-6$ and $k = - 36$.

Answer:

A. $(-6,-36)$