# 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?

3, -3; 6, -6; 9, -9; 36, -36

**Solution:**

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

It can be written as

y = x^{2} + 12x + 6

Now convert the standard form to vertex form. The vertex form of a parabola is y = a ( x − h ) ^{2} + k

First complete the squares and separate x^{2} and x terms.

y - 6 = x^{2} + 12x

y - 6 + (-12/2)^{2}= x^{2} + 12x+(-12/2)^{2}

Add 36 on both sides of the equation

y - 6 + 36 = x^{2} + 12x + 36

By further calculation

y + 30 = (x + 6)^{2}

So we get the vertex form as

y = (x + 6)^{2} - 30

Therefore, the zero pairs 36, -36 can be added to the function.

## 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?

3, -3; 6, -6; 9, -9; 36, -36

**Summary:**

The zero pair that could be added to the function f(x) = x^{2} + 12x + 6 so that the function can be written in vertex form is 36, -36

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