Parabola Reflections Explained (Why y=−x^2 Flips Upside Down)

Added: 2026-05-26

[00:00:00]the transformation difference between these two here. Everyone knows what y = x squared looks like, but what happens when we chuck a negative sign in front of it? If you chuck a negative sign in front of it, all it's doing is just changing all the y values into negative values. So, basically, imagine the parabola turning upside down. The way to remember this is a negative sign gives a sad face, and a positive one gives a happy face. It is simple as that at the end of the day. Just think of the old y value getting multiplied by -1, which causes a reflection over the x-axis, which creates that sad face.