The standard equation of a parabola :
(y-k) = a(x-h)². h and k being the coordinates of the vertex, then:
y-3 = a(x-0) → y = ax² + 3
Let's calculate a (from the table):
if x = 1 → y =2 Plug in y = ax² + 3
2 = a(1²)+3 → a = -1
And the equation becomes : y = - x² + 3
For x = 9 → y = - 78
For x = 10 → y = -97
Average rate of change = (y₂-y₁)/(x₂-x₁) = (-97+78)/(10-9) = - 19 (Answer A)