Polynomial Function Graphing Help

Let's do some Algebra, first

Letting x  = 0......the y intercept  is  at     - 3

We  have

1x^3  + 2x^2  - 3

Note that, if we add the ntegers in red and get 0, then 1 is a root  (an x intercept)

So  ( x - 1)  is a factor

To find if we have any other real roots....perform some polynomial division

            x^2  + 3x  + 3

x - 1  [  x^3  + 2x^2  +  0x   -   3  ]

            x^3  -  1x^2

          ______________________

                      3x^2  + 0x

                      3x^2   -  3x

                      ________________

                                 3x  - 3

                                 3x  - 3

                                 ______

The remaining polynomial  is    x^2  + 3x   + 3

The discriminant  is     3^2 - 4 (1) (3)  =  -3

Since this is < 0......we have no more real roots

So.....

The y intercept  is - 3

And the x intercept is  1

Here's the graph : https://www.desmos.com/calculator/kfgpcs3g09