Question

Which zero pair could be added to the function fon) = x2 + 12x + 6 so that the function can be written in vertex form?

03.-3
0 6.6
03-3
O 36,-36​

Answer 1

Last option: 36,-36​

Explanation:

The vertex form of the function of a parabola is:

`y=a(x-h)^2+k`

Where (h,k) is the vertex.

To write the given function in vertex form, we need to Complete the square.

Given the Standard form:

`y=ax^2+bx+c`

We need to add and subtract
`((b)/(2))^2` on one side in order to complete the square.

Then, given
`y=x^2+12x+6`, we know that:

`((12)/(2))^2=6^2=36`

Then, completing the square, we get:

`y=x^2+12x+(36)+6-(36)`

`y=(x+6)^2-30` (Vertex form)

Therefore, the answer is: 36,-36​

Answer 2

36,-36

EXPLANATION

The given function is:

`f(x) = {x}^(2) + 12x + 6`

To write this function in vertex form;

We need to add and subtract the square of half the coefficient of x.

The coefficient of x is 12.

Half of it is 6.

The square of 6 is 36.

Therefore we add and subtract 36.

Hence the zero pair is:

36, -36.

The correct answer is D.