Question

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

Answer 1

The most general proccedure for this type of problems is the following:

For a quadratic function of the following form
`f(x)=x^2+bx+c`; where b and c are real numbers.

1) Identify the value that accompanies the x, that is, the value "b"

2) Divide the value of b by 2 and then square it:
`((b)/(2))^2`

3) Add and subtract in the function the value of
`((b)/(2))^2`

4) Write the complete function of the form
`f(x) = (x+(b)/(2))^2-((b)/(2) )^2+c`

For the function presented
`f(x)=x^2 +12x+6` the result is as follows:

1) The value of b is 12

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

3)
`f(x)=(x^2+12x+36)-36+6`

4)
`f(x)=(x+6)^2-36+6`

Finally the function is:

`f(x)=(x + 6)^2-30`

The zero pair that must be added is 36 and -36