Question

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

Explanation:

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.