Surely you can graph this yourself?

Yes, the zeros are kind of ugly, aren't they? I get

As to how high it gets there are two ways depending on which class you are in.

1) Complete the square to put the quadratic in vertex form. The y value at the vertex is the highest point.

2) Use the first derivative of y to find the absolute maximum of the function.

A polynomial will have multiple zeros (or perhaps none at all!) if the degree of the polynomial is greater than 1. As far as non-polynomials are concerned I have no idea how to show this without actually solving for the zeros.

You are correct. "Naming" them simply means tell what they are.

-Dan