Question

Rewrite the function by completing the square.

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


f(x)=(x+__)^2=__

Answer 1

`y = x^2+14x +(14/2)^2 +8 - (14/2)^2`

And solving we got:

`y = x^2 +14x +49 + 8 -49`

And we can reorder the terms we got:

`y =(x+7)^2 -41`

And that would be the equivalent expression for the problem

Explanation:

For this case we have the following function given:

`y = x^2 +14x +8`

And we can complete the square adding the middle of 14 squared and subtracted before like this:

`y = x^2+14x +(14/2)^2 +8 - (14/2)^2`

And solving we got:

`y = x^2 +14x +49 + 8 -49`

And we can reorder the terms we got:

`y =(x+7)^2 -41`

And that would be the equivalent expression for the problem