Calculating Slope Functions

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 and check it using the input field. Write down both functions.
2. Compare the equations of the quadratic function f and the slope function g. Try to find out how the equation of the slope function can be calculated using the equation of f(x). Can you come up with a rule?
3. Check your rule for at least three different functions by changing the sliders for a, b, and c. Write down your examples.