Answer:
See below
Step-by-step explanation:
I assume you mean [tex]f(x) = 3(x-1)^2-4[/tex]
The equation is already in vertex form [tex]f(x)=a(x-h)^2+k[/tex] where [tex]a[/tex] affects how "fat" or "skinny" the parabola is and [tex](h,k)[/tex] is the vertex. Therefore, the vertex is [tex](h,k)\rightarrow(1,-4)[/tex].
The axis of symmetry is a line where the parabola is cut into two congruent halves. This is defined as [tex]x=h[/tex] for a parabola with a vertical axis. Hence, the axis of symmetry is [tex]x=1[/tex].
The minimum value is the smallest value in the range of the function. In the case of a parabola, the y-coordinate of the vertex is the minimum value. Therefore, the minimum value is [tex]y=-4[/tex].
The interval where the function is decreasing is [tex](-\infty,1)[/tex]
The interval where the function is increasing is [tex](1,\infty)[/tex]
