Final answer:
The equation of the given parabola in vertex form is y = 1/8x^2 - 2.
Step-by-step explanation:
To write the equation of a parabola in vertex form, we use the formula y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Given that the vertex is (0, -2), we substitute h = 0 and k = -2 into the equation and get y = a(x-0)^2 - 2 or y = ax^2-2.
To determine the value of 'a', we substitute the coordinates of the point (12, 16) into the equation:
16 = a(12)^2 - 2
16 = 144a - 2
144a = 18
a = 18/144 = 1/8
Therefore, the equation of the parabola in vertex form is y = 1/8x^2 - 2.