Equation of a Slope Function

Below you can see the graphs of a quadratic polynomial f(x) = a x² + b x + c and its slope function.

1. Find the equation of the slope function. Write down the quadratic function f(x) as well as your slope function g(x).
2. Check your answer by typing your slope function's equation g(x) = ... into the input field. Hit the Enter-key. Tip: If your answer is not correct you can change it by double clicking on g(x).
3. Click on the little ellipse-icon in the upper right corner to reset the construction. Move the sliders to match the following values: a = −1, b = 4, and c = 2. Repeat steps (1) and (2).