Quadratic / Piecewise Functions Compare and Contrst

1. A Quadratic function is one of the form f(x)=ax^2+bx+c where a, b, and c are numbers with a not equal to zero.

2. There is a U shaped curve used to graph Quadratic functions called a parabola.

3. Quadratic functions are identified by whether they are greater or less than zero which identifies the opening of the parabola.

4. A piecewise function is a function defined by sub functions, and each sub-function applying to a certain interval of the main function's domain (a sub-domain).

5. Piecewise functions may also be differentiable on their domains.

6. Functions are called piecewise continuous on an interval if the interval can be broken into a finite number of subintervals on which the function is continuous on each open subinterval (i.e. the subinterval without its endpoints) and has a finite limit at the endpoints of each subinterval.