Question

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

Answer 1

f(x) = x² + 12x + 6  → y = x² + 12x + 6

Let us convert the standard form into vertex form.

1) Complete the squares. Isolate x² and x terms.
y - 6 = x² + 12x

2) Create the perfect square trinomial. Whatever number is added on one side must also be added on the other side. 

y - 6 + 36 = x² + 12x + 36
y + 30 = (x + 6)²
y = (x + 6)² - 30  ← Vertex form

To check:

y = (x + 6) (x + 6) - 30
y = x² + 6x + 6x + 36 - 30
y = x² + 12x + 6

The zero that could be added to the given function is 36, -36