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'.
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#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#
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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.