1. find the equation of the axis of symmetry and the coordinates of the vertex of the function: y=〖3x〗^2-2

I see y = 3x^2 - 2.  If that is the case, there is no movement indicated in the x direction at all, only the y direction. If there was movement along the x axis, there would be a number inside a set of () with the x, like this: (x-3)^2. But that is not there in your case, so the x coordinate of the vertex stays right where it starts, at the origin, or x = 0. The "minus 2" indicates y movement: down 2 units. So the vertex sits at (0, -2). The axis of symmetry is the same as what the x coordinate is, but in equation form. So the axis of symmetry has an equation of x = 0.