How do you use the important points to sketch the graph of #y=-3x^(2)#?

#color(blue)("Important if you wish to understand a quadratic")#

First lets consider the influence on #y=x^2# by the parts in #y=ax^2+bx+c#

The #c# part lifts the graph up or down according to its value and sign.

The #bx# part moves the graph left or right.
If negative it moves the graph such that it is more positive (normally moves right)

If positive it moves the graph such that it is more negative (normally moves left)

The negative effect on #x^2 ->-3x^2#
If it is positive the graph is of form #uu#
If it is negative the graph is of form #nn#

The effect of the 3 in front of #-3x^2#
This makes the graph look as though it is narrower
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

Write as:

#y=-3x^2+0x+0#

The constant #c=0# so the vertex is tangential to the x-axis and does not cross it.

The #0x# means that the x-axis is the axis of symmetry

The negative #(-1)xx3x^2# means that the graph is of form #nn#.

The word #ul("'sketch'")# is very important.

It means you do not have to be precise. So as long as your #uu# looks symmetrical about the x-axis and the vertex (bottom of the curve) looks as though it passes through the origin you will be ok.

Make sure you label everything. Gets you extra marks.