Enlarging or reducing parabolas

If you enlarge or reduce a parabola you make it steeper or flatter and there are four elements you need to remember.

$y=2x^2$ - Doubles the distance from the $x$ axis.

$y=1/2x^2$ - Halves the distance from the $x$ axis.

$y=(2x)^2$ - Halves the distance from the $y$ axis.

$y=(1/2x)^2$ - Doubles the distance from the $y$ axis.

We can remember this by using the following chart:

How to enlarge or reduce parabolas using this chart

Note also that

$y=3x^2$ - Triples the distance from the $x$ axis.

$y=1/3x^2$ - Thirds the distance from the $x$ axis.

$y=(3x)^2$ - Thirds the distance from the $y$ axis.

$y=(1/3x)^2$ - Triples the distance from the $y$ axis.

$y=x^2$

$y=x^2$ should be plotted as: