How do I sketch the curve y = (x+1)((1)/(3)x2 + (1)/(3)x - (2)/(3))?

To sketch the curve $y = (x+1)(\frac{1}{3}x^2 + \frac{1}{3}x - \frac{2}{3})$, we first simplify and find key features: x-intercepts, y-intercept, turning points, and end behavior.

Step 1: Simplify the equation.
Factor out $\frac{1}{3}$ from the second parenthesis:

$$y = (x+1) \cdot \frac{1}{3}(x^2 + x - 2)$$

Factor the quadratic term $x^2 + x - 2$:

$$x^2 + x - 2 = (x+2)(x-1)$$

So the equation becomes:

$$$$