Question

how to graph y=x^3-3x^2?

Answer 1

I won't go step by step, just discuss the gist.

You'll want to find the points of interest. Manipulating it often make them clearer:

y = x^2(x - 3)

which tells us that the function = 0 when x = 0 and x = 3.

From experience, you'll know these are pretty much the only points to worry about (and those in between)

so you'll want to plug in a few points before x = 0, between x= 0 and x = 3 and then after x = 3; to notice whether they are positive or negative.

Note: Since the function has two roots, it means that the function curves at some point (where the derivative = 0; you can find that x value)
You'll use the points where the derivative = 0 as other ranges to look at (what happens before and after)

i feel like this is getting long and rambly so ill stop lol, hope it helps ^_^

Answer 2

Thank u soooo much:)