Question

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

Answer 1

Answer:

Please check the explanation.

Step-by-step 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

$\frac{2ax}{2x}=\frac{8x}{2x}$

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,

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