Verified Answer :

frika

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.

JeanaShupp

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)

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