Question

a firework is modelled by the relation h=-4.9(t-9)^2+170 h=height above ground in metres and t=time in seconds
what are the co-ordinates of the vertex of this parabola?

Answer 1

h = (t-9)^2 + 170

h is least when t = 9s
The value of h there is 170.

The vertex is therefore at
t = 9; h=170

Answer 2

your equation
h=-4.9(t-9)^2+170

is in the standard form of the "vertex" form of a quadratic function,
the vertex is (9, 170)

[standard form ...
if y = a(x-h)^2 + k , the vertex is (h,k) ]