Write the equations of two different polynomial functions with odd symmetry, the graphs starting in quadrant 2, and with the following as some of their features: TP at x=2, IP at x=-5

Question

PLease help, I have no idea how to solve this

Answer 1

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:

g(x)=-(x+5)⁵(x+12)⁴(x-2)⁴/100.

Note that -5 lies midway between -12 and 2, two of the turning points.