Question

Which zero pair could be add into the function f(x)=x^2+12x+6 so that the function can be written in vertex form

Answer 1

We need a perfect square, and we start with

$x^2+12x$

This means that the binomial begins with $(x+\ldots)^2$, and $12x$ is the double product of $x$ and the number we're looking for. So, that number is $6$. Since

$(x-6)^2 = x^2-12x+36$

we need to add $30$ (and subtract it to leave the expression untouched. So, we have

$x^2-12x+6 = x^2-12x+6 + 30 - 30 = (x-6)^2 - 30$