Question

How do you use the important points to sketch the graph of `y = -1/3x²`?

Answer 1

graph{-(1/3)x^2 [-27.59, 27.98, -15.53, 12.27]}
for tracing any graph you should scrounge some points.

Explanation:

1) put some simple values of x and obtain y like, here, at x=0, y=0
at x= `+-1`, y= -`1/3`
at x`rarr +-infty`, y`rarr -infty`
2) check for maxima and minima of function using derivative.
3) also put some simple points like at x=`+-1,+-3,` and find y
4) interchange x and y, if no change appears it means the `f(x)` is symmetrical about line x=y
With little practice I hope you will be able to trace curves.