The vertex of g(x) = [tex]\rm 3x^2 - 12x + 7[/tex] is (2, -5), the correct option is C.
The vertex of a parabola is the highest or lowest point, also known as the maximum or minimum of a parabola.
The standard equation of the vertex of the parabola is;
[tex]\rm a(x - h)^2 + k[/tex]
Where h and k are the coordinates of the vertex of the parabola.
The given expression is;
[tex]\rm =3x^2 - 12x + 7\\\\= 3(x^2 - 4x) + 7\\\\ = 3[ (x - 2)^2 - 4)] + 7\\\\= 3(x - 2)^2 - 12 + 7\\\\= 3(x - 2)^2 - 5[/tex]
On comparing with the standard form of vertex of the parabola
h = 2 and k = -5
Hence, the vertex of g(x) = [tex]\rm 3x^2 - 12x + 7[/tex] is (2, -5).
To know more about parabola click the link given below.
https://brainly.com/question/20333425
