The vertex is the point (-6,-30)
Vertex form of Parabola
Parabola is a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the cone or by the locus of points equidistant from a fixed line and a fixed point not on the line.
The equation of a vertical parabola in vertex form is equal to
[tex]$f(x)=a(x-h)^{2}+k$[/tex]
where
a is a coefficient
[tex]$(\mathrm{h}, \mathrm{k})$[/tex] is the vertex
we have
[tex]$\tex{ f) } x)=x^{2}+12 x+6$[/tex]
Convert to vertex form
Complete the square
[tex]&f) x)-6=x^{2}+12 x \\[/tex]
[tex]&f) x)-6+36=\left(x^{2}+12 x+36\right) \\[/tex]
[tex]&f) x)+30=\left(x^{2}+12 x+36\right) \\[/tex]
[tex]&f) x)+30=(x+6)^{2} \\[/tex]
[tex]&f) x)=(x+6)^{2}-30[/tex]..............equation in vertex form
Therefore,
The vertex is the point (-6,-30)
[tex]&\mathrm{h}=-6, \mathrm{k}=-30[/tex]
To know more about vertex form refer to:
https://brainly.com/question/15165354
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