Question

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

(–6, –36)
(–6, 0)
(6, 0)
(6, –36)

Answer 1

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.

Answer 2

Answer: (–6, –36)

Step-by-step 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)