In this lesson, students learned about solving equations involving quadratic functions and simplifying expressions. The instructor demonstrated how to evaluate the function ( g(x) = 2x^2 – 10 ) at different points, such as ( x = -2 ), and the method to simplify expressions like ( f(x + 2) – f(x) ), aiming to prove the claim for ( x + 8 ). Additionally, the lesson covered examples of solving quadratic functions and highlighted their practical applications in various contexts.