I need to find the vertex, axis of symmetry, and if the graph will open upward or downword

f(x)=-3x^2-5

There's gotta be a review section in your text that says:

y - (-5) = -3(x-0)^2
so vertex = (0,-5)

axis of symmetry = -b/2a = 0/-6 = 0

since the coefficient of x^2 < 0, it opens downward.