Question

tell whether graph opens upward or downward. then find the axis of symmetry and vertex of graph of function y=-x^2+9

Answer 1

coeff of x^2 = -ve
Therefore, it opens downward.
axis of symmetry = -b/2a = 0
vertex = (0,9)

Answer 2

let's consider the graph having a form
y= a(x-h)^2 +k
If a>0, it opens upwards and vice versa
Axis of symmetry is x=h
vertex is (h,k)
consider your case,
y=-x^2+9 can be rewritten as y= (-1)(x-0)^2 +9
So a<0, it opens downwards
h=0, so axis of symmetry is x=0
k=9, so the vertex is at (0,9)