Quadratic Transformations Explained (How to Describe Any Parabola Quickly)

Added: 2026-06-02

[00:00:00]Describe this graph. When we get given something like this, we actually know entirely how to draw it straight away.

[00:00:05]The quadratic is already in turning point form. We can see it's been shifted horizontally by one unit. It's been shifted up vertically by three units.

[00:00:13]The coefficient of two changes the vertical stretch of the parabola, but generally it's still going to be shifted one unit over to the right and three units up. So, we know straight away it looks like this here. And because it's a positive in front of everything, we know it's going to open upwards, which means it doesn't have any x-intercepts, but it does have a y-intercept. Using stuff to describe this, I would say it'd be shifted to the right by one, up by three units, vertically stretched by a factor of two, and it just opens upwards as well.