Graphing e field for ring charge

[pyroknife]

Homework Statement

E=(kqz)/(z^2+a^2)^1.5 Through calculus i found that the max occurs at z=a/sqrt(2) and z=-a/sqrt(2) and I think the negative one is the minimum. That answer was given in the book also. The ring has radius a. It wants me to graph E versus z. I'm a little confused on how to graph this. the only 2 points I have on there are 1 max and 1 min but I don't know how to draw the general shape.

Homework Equations

The Attempt at a Solution

 

[ehild]

There are two points you know: the places of maximum and minimum. What is E at z=0? What is the sign of E at negative values of z? Where is E=0? What are the limits at infinity and at -infinity? From these, you can sketch the curve.

ehild