In the right hand panel is a quadratic function in the form [b]f(x) = x² + px + q[/b][br]The two parameters p and q determine the parabola. [br][br]The p,q plane is shown in the left hand panel with the point p,q plotted.[br][br]Drag the point around the p,q plane by sliding the large BLUE tick marks on the axes. What happens in the right hand x,y plane?[br][br]Why do the point and the parabola change color? Where are they RED? GREEN?[br][br][size=150][b]Challenge[/b][/size] - [br] What is the shape of the red/green boundary in the p,q plane?[br][br] In the p,q plane, the boundary can be thought of a a function q(p).[br][br] What is this function? How is it related to the discriminant of the quadratic?[br][br][size=150][b]Challenge[/b][/size] – [br] The locations of the real or complex conjugate roots of the quadratic appear [br] in the right hand panel as large gold dots. Trace the complex roots in the x,y plane.[br][br] Can you formulate a conjecture about the path they take as you move the point in[br] the p,q plane along a horizontal line? along a vertical line? [br] [br] Can you prove or disprove your conjectures?