Write the vertex form of the equation of the parabola which has a vertex of (0,0) and contains the points (2,-2)

Vertex Form: y = a(x - h)² + k

Vertex: (h,k)
y = a(x - 0)² + 0 

Point: (2,-2) ⇒ x = 2; y = -2
-2 = a(2 - 0)² + 0

Solve: 

     -2 = a(2 - 0)² + 0
     -2 = a(2)² + 0
     -2 = a(4) + 0
    - 0             - 0

     -2 = a(4)

   -2      =     4a
         
    4              4
     
       a = -1/2 

Plug "a" value into vertex form : y = -1/2(x - 0)² + 0
Final y = -1/2x 

(The plus 0 does not need to be included in the final answer)

I hope my answer is correct, but I am not 100% sure. Hope I could help in some sort of way.