Respuesta :

kudzordzifrancis

ANSWER

36,-36

EXPLANATION

The given function is:

[tex]f(x) = {x}^{2} + 12x + 6[/tex]

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.

luisejr77

Answer:

Last option: 36,-36​

Step-by-step explanation:

The vertex form of the function of a parabola is:

[tex]y=a(x-h)^2+k[/tex]

Where (h,k) is the vertex.

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

Given the Standard form:

[tex]y=ax^2+bx+c[/tex]

We need to add and subtract [tex](\frac{b}{2})^2[/tex] on one side in order to complete the square.

Then, given [tex]y=x^2+12x+6[/tex], we know that:

[tex](\frac{12}{2})^2=6^2=36[/tex]

Then, completing the square, we get:

 [tex]y=x^2+12x+(36)+6-(36)[/tex]

[tex]y=(x+6)^2-30[/tex] (Vertex form)

Therefore, the answer is: 36,-36​

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