What is the vertex and direction of this parabola ##y=-3(x+2)^2+3##?

A parabola in the form: ##y = a(x – h)^2+k## will open up if a > 0, and down if a < 0. Since a = -3 in your example, the parabola will open down and have a maximum at the vertex. In the form ##y = a(x - h)^2+k##, (h,k) is the vertex. In your example, then, (-2,3) is the vertex. The maximum value is 3. Observe the graph below:

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