1. what is the difference between the rate of change for a linear function and the rate of change for a…

Brief Explanations:

A linear function (y = mx + b) has a constant rate of change (slope (m)). A quadratic function (y=ax^{2}+bx + c) has a non - constant rate of change. The average rate of change of a quadratic function over an interval ([x_1,x_2]) is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{a(x_2^{2}-x_1^{2})+b(x_2 - x_1)}{x_2 - x_1}=a(x_1 + x_2)+b), which depends on the values of (x_1) and (x_2).

Answer:

The rate of change of a linear function is constant (equal to its slope), while the rate of change of a quadratic function is non - constant and varies depending on the interval considered.