How do you graph `y=3x²`?

`color(blue)("General comments")`

The general shape of quadratics is `uu"; "nn"; "sub"; "sup`

However `sub` and `sup` are special cases. The main thing to remember is that it is a bit like the horse shoe shape.

Most of the ones you come across will be of shape type `uu` and `nn`.

The turning point has a specific name and that is 'vertex'.

The line that 'goes up the centre' for type `uu and nn` is called 'the axis of symmetry'.

The line that goes across the centre of types `sub and sup` is also called 'the axis of symmetry'.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Thinking about specific points/shape")`

With this particular equation you should note that if `x` is 0 then:
`y=3xx0^2 = 0`

Given that `x` is zero when `y` is zero this mat be shown as:
`(x,y)->(0,0)` This is called an ordered pair and this case is the 'vertex'. As the line of symmetry passes through the vertex then this particular graph is symmetrical about the y-axis

As `3x^2` is positive the shape is that of `uu`

Note that `color(red)("if")` it had been negative then the graph would have had the shape of `nn`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
One way would to build a table of values, mark them on the paper and then join up the dots as neatly as you can with a curve.

As we know the vertex is at (0,0) we should include that point in our table. These are values I choose. You may choose others if you wish.