QUADRATIC functions - parameter Plane

In the right hand panel is a quadratic function in the form f(x) = x² + px + q[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 YELLOW tick marks on the p and q 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]Challenge - 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] What is this function? How is it related to the discriminant of the quadratic?[br][br]Challenge – The locations of the real or complex conjugate roots of the quadratic appear in the right hand panel as large gold dots. [br] Trace the complex roots in the x,y plane. [br] Can you formulate a conjecture about the path of the roots as you move the point in the p,q plane along a horizontal line? along a vertical line? [br] Can you prove or disprove your conjectures?[br][br][color=#ff0000][i][b]What questions could/would you put to your students based on this applet ?[/b][/i][/color]

Information: QUADRATIC functions - parameter Plane