How to Graph a Quadratic Piecewise Function

The video tutorial explains how to graph a quadratic piecewise function, H(x), with two parts: 3 - x^2 for x ≤ 0 and x^2 + 2 for x > 0. The instructor demonstrates how to graph each part separately, using tables to plot points and ensuring the correct use of open and closed circles to represent constraints. The importance of understanding piecewise functions and their constraints is emphasized, ensuring the function passes the vertical line test.

What is the importance of constraints in a piecewise function?

What happens if both functions in a piecewise function are true at the same point?

Describe the process of creating a table to graph a piecewise function.