This problem illustrates how you can embed Java applet code in a WeBWorK example to create an interactive homework problem that could never be provided by a text book.

WeBWorK can use existing javaScript and Java code to augment its capabilities.

mathbean applet from David Ecks

The graph above represents the function $$f(x) = x^2 + a x +b$$ where $a$ and $b$ are parameters.

For each value of $a$ find the value of $b$ which makes the graph just touch the x-axis.
if a= 3 then
if a= 0 then
if a= -2 then

Does this relationship between a and b specify b as a function of a? (Yes or No)
Does this relationship between a and b specify a as a function of b? (Yes or No)
Write a formula for calculating this value of $b$ from $a$.
b =