Answer:
The vertex is the point (-6,-34)
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
In this problem we have
[tex]y=x^{2}+12x+2[/tex]
Convert in vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y-2=x^{2}+12x[/tex]
Complete the square . Remember to balance the equation by adding the same constants to each side.
[tex]y-2+36=x^{2}+12x+36[/tex]
[tex]y+34=x^{2}+12x+36[/tex]
Rewrite as perfect squares
[tex]y+34=(x+6)^{2}[/tex]
[tex]y=(x+6)^{2}-34[/tex]
The vertex is the point (-6,-34)
