- #1

opus

Gold Member

- 717

- 131

So for a polynomial function, the behavior of the graph at the zeros is determined by the evenness or oddness of the magnitude of the zeros. If the magnitude is odd, the graph will cross the zero. If the magnitude is even, it will bounce at the zero. Why is this true? What specifically causes these different actions?

Also, I'm trying to figure out why even degree functions look like a parabola, but odd degree functions look like an S shape? I understand what causes the parabola, but I'm not sure what causes the S shape. What causes it to steadily climb, then decrease the rate at which it climbs, then goes back to climbing again at the original rate?

Thanks for reading!