Find the equation of the parabola whose axis is horizontal, vertex on the y-axis and which passes through (2,4) and (8,-2)

axis is horizontal, vertex on the y-axis, so

x = ay^2 + h
so,
16a+h = 2
4a+h = 8
solve for a and h, and we have
x = -1/2 y^2 + 10