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: $(\frac{b}{2})^2$

3) Add and subtract in the function the value of  $(\frac{b}{2})^2$

4) Write the complete function of the form $f(x) = (x+\frac{b}{2})^2-(\frac{b}{2} )^2+c$

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

1) The value of b is 12

2) $(\frac{12}{2} )^2=36$

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