Rate of Change for a Quadratic Function

Let $f$ be a quadratic function defined by $f(x) = a*x^2 + b*x + c$. Consider the following statements.

I. The average rate of change of $f$ over the interval $[x_1, x_2]$ is given by $a*(x_1+x_2)+b$.

II. If $a = 0$, the average rate of change of $f$ is constant for any interval.

III. For an interval with endpoints symmetric about the vertex of the graph of $f$, the instantaneous rate of change at the midpoint of the interval equals the average rate of change over the interval.

Which of the statements is or are true?