Question

What is the vertex of the function f(x) = x2 + 12x?

(–6, –36)
(–6, 0)
(6, 0)
(6, –36)

Answer 1

Answer: (–6, –36)

Explanation:

We know that to convert a quadratic form
`y=ax^2+bx+c` to vertex form
`y=a(x-h)^2+k` where (h,k) is the vertex , we use the method of completing the square.

Given function=
`x^2+12x`

Which can be written as :

`x^2+12x=x^2+2(x)(6)`, adding and subtracting square of 6, we get

`x^2+2(x)(6)+(6)^2-(6)^2\\=(x+6)^2-6^2\\=(x-(-6))^2-36`

On comparing with the standard vertex form we get,

Vertex =(–6, –36)

Answer 2

Consider the function
`f(x) = x^2 + 12x.`

You can rewrite it as

`f(x) = x^2 + 12x=x^2+2\cdot x\cdot 6=x^2+2\cdot x\cdot 6+6^2-6^2=(x+6)^2-36.`

When x=-6,

`f(-6)=(-6+6)^2-36=36.`

The vertex is (-6.-36).

Answer: correct choice is A.