Question

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

Answer 1

`\implies f(x) = ( x + 2)^2`

Explanation:

Given :-

• f(x) = x² + 8x + 4 .

And we need to rewrite the function by completing the square. The function is ,

`\implies f(x) = x^2+8x + 4`

• We can rewrite the function in the form of ,

`\implies ( a + b)^2= a^2+b^2+2ab`

Rewriting the function :-

`\implies f(x) = x^2+8x + 4\\\\\implies f(x) = x^2 + 2.2.2x + 2^2`

• This is similar to the whole square form stated above . So ,

`\implies f(x) = ( x + 2)^2`

Hence the function in whole square form is (x + 2)² .