we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex
if [tex]a > 0[/tex] -----> then the parabola open upward (the vertex is a minimum)
if [tex]a < 0[/tex] -----> then the parabola open downward (the vertex is a maximum)
The axis of symmetry is equal to
[tex]x=h[/tex]
In this problem let's analyze two cases
First case
[tex]f(x)=3(x-2)^{2}+4[/tex]
the vertex is the point [tex](2,4)[/tex]
[tex]a=3[/tex]
so
[tex]3 > 0[/tex] -----> then the parabola open upward (the vertex is a minimum)
The axis of symmetry is equal to
[tex]x=2[/tex]
Second case
[tex]f(x)=3(x-2)^{2}-4[/tex]
the vertex is the point [tex](2,-4)[/tex]
[tex]a=3[/tex]
so
[tex]3 > 0[/tex] -----> then the parabola open upward (the vertex is a minimum)
The axis of symmetry is equal to
[tex]x=2[/tex]
