Move the point A along the quadratic equation and watch the trace draw the derivative function. Adjust the sliders to adjust the quadratic equation and hence see what effect this has on the derivative function. Regardless of the quadratic you should realise that the derivative of a quadratic function is a linear function.
Q1. What type of function is the derivative of a quadratic? Q2. When a is positive has the derivative function got a positive or negative slope? Why? Q3. When a is negative has the derivative function got a positive or negative slope? Why?