Question

Complete the square to transform the expression x2 + 4x + 2 into the form a(x − h)2 + k.

Answer 1

The transformation of  $x^2+4x+2$ is  $1(x-(-2))^2+(-2)$  .

Step-by-step explanation:

Here we need to Complete the square to transform the expression x2 + 4x + 2 into the form a(x − h)2 + k.Let's find out:

We have equation  x2 + 4x + 2  or , $x^2 + 4x + 2$ . Let's simplify it to a(x − h)2 + k

⇒ $x^2+4x+2$

⇒ $(x^2+4x+2)+4-4$

⇒ $(x^2+4x+4)+2-4$

⇒ $(x^2+4x+4)-2$

⇒ $(x+2)^2-2$

⇒ $(x-(-2))^2-2$

⇒ $1(x-(-2))^2+(-2)$       ........ (1)

Comparing equation (1) with $a(x - h)^2 + k$ we get :

$a= 1\\h = -2\\k = -2$

Therefore , The transformation of  $x^2+4x+2$ is  $1(x-(-2))^2+(-2)$  .