Question

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

Answer 1

y=(x+3)^2-6 Hope This Helps

Answer 2

`f(x)=(x+3)^(2)-6`

Explanation:

we have

`f(x)=x^(2) +6x+3`

we know that

The equation of a vertical parabola into vertex form is equal to

`f(x)=a(x-h)^(2)+k`

where

(h,k) ------> is the vertex of the parabola

Convert the function into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`f(x)-3=x^(2) +6x`

Complete the square. Remember to balance the equation by adding the same constants to each side

`f(x)-3+9=x^(2) +6x+9`

`f(x)+6=x^(2) +6x+9`

Rewrite as perfect squares

`f(x)+6=(x+3)^(2)`

`f(x)=(x+3)^(2)-6` -----> function in vertex form