Question

Given ​ f(x)=x^2+12x+26 ​.

Enter the quadratic function in vertex form in the box.

f(x)=

Answer 1

f (x) = (x+6)^2 - 10

Explanation:

Answer 2

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
`(12)/(2)=6` then 6^2 = 36

Add and subtract 36 to complete the square

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

`image`

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