I have finished this problem but I'm not quite sure if this has 2 answers or 1. Here is the question.

Find the points on the parabola y= 9/2 - x^2 that are closest to the origin.

Steps I did:

Use the distance formula and got x^2 + (9/2 - x^2)^2

S'= 4x(x^2 - 4)

x = 0, x = +-2

Points I got: (-2, 1/2), (2, 1/2)

is there something I did wrong?