f(x)=x^3+x^2-2x=x(x^2+x-2)=x(x+2)(x-1)
The y intercept is when x=0, so y=0 (origin); the x intercept is when y=0, so x(x+2)(x-1)=0, so x=0 (origin), 1 and -2.
The gradient or slope is f'(x)=3x^2+2x-2 and is zero at a turning point. Using the formula to solve the quadratic:
x=(-2+sqrt(4+24))/6=(-1+sqrt(7))/3=0.5486 and -1.2153 (approx). The coords of the turning points are (0.5486,-0.6311) and (-1.2153,2.1126). The nature of these turning points is given by f"(x)=6x+2, which is positive (minimum) at the first turning point and negative (maximum) at the second.
The graph zigzags by starting in the negative quadrant (QIII) crossing the x axis at -2 to QII, reaching a maximum at the second turning point, passing through the origin to reach the minimum at the first turning point in QIV, and crossing the x axis again at 1 to continue rising in QI.