Question

Given ​ f(x)=x^2+12x+26 ​.

Answer 1

f(x)=x^2+12x+26

Vertex form of f(x) = a(x-h)^2 +k

We change f(x) into vertex form using completing the square method

$f(x)=x^2+12x+26$

We take half of square of middle term

middle term is 12

Half of square of 12 is $\frac{12}{2}=6$ then 6^2 = 36

Add and subtract 36 to complete the square

$f(x)=(x^2+12x+36)+26-36$

$f(x)= (x+6)^2 +26 - 36 f(x)= (x+6)^2 -10$

The vertex form $f(x)= (x+6)^2 -10$