Find the difference quotient for a quadratic in standard form

The video tutorial explains the process of deriving a mathematical formula by substituting values, simplifying expressions, and correcting arithmetic mistakes. It emphasizes the importance of careful subtraction of terms and demonstrates how to finalize the limit to derive the equation of a line. The tutorial concludes with a validation of the derived equation.

How does the speaker simplify the expression after factoring out common terms?

What is the final equation of the line derived from the calculations?