Parabolic Equation & finding points?

Question

 A parabolic swing design is modeled by the equation (x-2)^2=1/2(y-1). if a horizontal support bar is placed 32 feet above the vertex of the swing find the points were the support bar intersects the swing on the coordinate plane. 

Answer 1

(y-1) = 2(x-2)^2

y = 2(x-2)^2 + 1 in vertex form vertex = min = (h,k) = (2,1)

if y = 32 ft, then 32 = 2(x-2)^2 +1

16 = (x-2)^2 +1

(x-2)^2 = 15

x -2 = +/-sqr15

x = 2+sqr15 or 2-sqr15