Quadratic equations are polynomial equations with one variable where the highest power of the variable is 2, and they can be solved using various methods, including factoring, completing the square, and the quadratic formula. The quadratic formula is a powerful tool that can be used to solve any quadratic equation, regardless of whether it can be factored or not, and it provides a direct solution for the variable x. The discriminant, represented by the expression (b² - 4ac), plays a crucial role in determining the nature of the solutions, indicating whether the equation has two distinct real roots, one real root, or two complex roots.

Theorems are proven statements in math, like building blocks for understanding complex ideas. Proofs are logical arguments that show why a theorem is true, and they are like learning the rules of a game before you can play. Learning to do proofs takes practice and patience, and the more you practice, the better you’ll understand the subject.

Equations are like puzzles where you need to find the missing piece, which is represented by a variable. You can solve equations using mental math, patterns, or inverse operations. Understanding equations and variables is important in many areas of math and science