Which function in vertex form is equivalent to f(x) = x2 + 6x + 3?

Solution:

The vertex form of the equation is given by

f(x) = a(x - h)2 + k

Given, f(x) = x2 + 6x + 3

Converting to vertex form,

x2 + 6x + 3 = x2 + 6x + 3 + 9 - 9

f(x) + 9 = (x + 3)2 + 3

Subtracting 9 on both sides 

f(x) =  (x+ 3)2 + 3 - 9

So we get

f(x) =  (x + 3)2 - 6

Therefore, the equation in vertex form is  f(x) = (x + 3)2 - 6.

Which function in vertex form is equivalent to f(x) = x2 + 6x + 3?

Summary:

The function f(x) = (x + 3)2 - 6 in vertex form is equivalent to f(x) = x2 + 6x + 3.

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