A parabola has a vertex (4,2) and

contains the point (-2,26). what is the equation of the parabola?

(x-4)^2 = k (y-2)

x^2 - 8 x + 16 = k y - 2 k
put in (-2,26)

4 + 16 + 16 = k(26) -k(2)

36 = 24 k
k = 36/24 = 3/2
so

x^2 - 8 x + 16 = 3/2 y - 3

2 x^2 -16 x + 32 = 3 y -6

3 y = 2 x^2-16 x + 38

y = (2/3) x^2 -(16/30 x + 38/3