Which of the following graphs could represent a 6th-degree polynomial function, with 3 distinct zeros, 1 zero with a multiplicity of 2, 1 zero with a multiplicity of 3, and a negative leading coefficient?

Question

mathmale · Answer

A 6th degree poly should give you 6 zeros.

Of these 6, 3 must be distinct.  This means you'll have exactly 3 points on the horizontal number like where the graph either crosses or touches the horizontal axis.

If a zero has a multiplicity of 2, that means the graph will loop either up or down and that its vertex will only touch (not cross) the horiz. axis.

If ... a multiplicity of 3, the graph will actually cross the horiz axis at that x-value.

mathmale · Answer

Could you possibly post illustrations of the four graphs that represent possible answers?