An example is f(x)=-(x+5)³(x+12)²(x-2)².
There is an inflection point at x=-5 and a turning point at x=2.
The function has odd symmetry about x=-5. The negative sign ensures the function starts in quadrant 2.
Another function can be obtained by replacing the cube with another odd power, and the squares by even powers. A constant can be used to amplify (or reduce) the whole expression. For example:
Note that -5 lies midway between -12 and 2, two of the turning points.