Identify the vertex and the Axis of Symmetry (AOS) in the quadratic function \[ f(x)=\frac{-2}{3}(x-1)^{2}+4 \] vertex \( (-1,-4) ; \operatorname{AOS} x=-1 \) vertex ( 1,4 ); \( \operatorname{AOS} x=1 \) vertex \( (1,-4) ; \) AOS \( x=-4 \) vertex \( (-1,4) ; \operatorname{AOS} x=-1 \)

The vertex of the given quadratic function \( f(x) = \frac{-2}{3}(x-1)^{2}+4 \) can be identified directly from its vertex form. The vertex is at the point \( (1, 4) \). The Axis of Symmetry (AOS) runs vertically through the x-coordinate of the vertex, hence the AOS is given by \( x = 1 \). It's essential to remember that any quadratic function in vertex form, \( f(x) = a(x-h)^2 + k \), reveals its vertex at the point \( (h, k) \). So, in this case, \( (1, 4) \) tells us precisely where the peak (or trough) of the parabola lies, and knowing that the AOS is always \( x = h \) means you’ll have a quick reference for the symmetry of the graph!