Finding point closest to origin

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?(Thinking)

Re: Finding point closest to origin

For some arbitrary point on the parabola , the square of the distance from this point to the origin is:

Implicitly differentiating. we find:

Since the denominator has no real roots, our only critical values are:

and the first derivative test shows that minima occur at . Since the distance function is even, we know the two points are the same distance from the origin, so we include them both.

You did well! :)