Question

Rewrite the function by completing the square. f(x)= x^2 +8x+4 ​

Answer 1

Please check the explanation.

Explanation:

Given the function

`f\left(x\right)=\:x^2\:+8x+4`

Let's rewrite the function by completing the square.

`0=x^2+8x+4`

Subtract 4 from both sides

`x^2+8x+4-4=0-4`

Simplify

`x^2+8x=-4`

Rewrite in the form (x+a)²=b

`x^2+8x=-4`

Rewrite in the form x²+2ax+a²

solve for a, 2ax = 8x

`2ax=8x`

Divide both sides by 2x

`(2ax)/(2x)=(8x)/(2x)`

simplify

`a = 4`

Add a²=4² to both sides

`x^2+8x+4^2=-4+4^2`

`x^2+8x+4^2=12`

Apply perfect square formula

(a+b)²= a²+2ab+b²

`\left(x+4\right)^2=12` ∵
`x^2+8x+4^2=\left(x+4\right)^2`

Thus,

`\left(x+4\right)^2=12`