Rewrite the function by completing the square.

f (x) = x^2 + 14x + 8

f (x) = (x + 7) ^2 - 41

Step-by-step explanation:

f (x) = x^2 + 14x + 8

We take half of the coefficient of the x-term and square it.

Half of 14 is 7. 7 squared is 49. We add 49 to complete the square, but we then must subtract it at the end to not change the value of the function.

f (x) = x^2 + 14x + 49 + 8 - 49

f (x) = (x + 7) ^2 - 41