Algebra 1 – Unit 8 – Quadratic Equations

Unit 8 – Solving Quadratic Equations

Algebra 1 - Unit 8 lays the foundation for understanding and solving quadratic equations, which are polynomials of degree two. One of the critical skills acquired in this course is factoring trinomials. This involves expressing a quadratic expression as a product of two binomials, which is essential for solving quadratic equations by setting each factor to zero. Special cases, such as perfect square trinomials and the difference of squares, provide shortcuts that simplify the factoring process. Additionally, the quadratic formula is introduced as a powerful tool for finding the roots of any quadratic equation, especially when factoring is not possible.  This formula, derived from completing the square, allows for a straightforward calculation of solutions using the coefficients of the equation. Moreover, systems of equations involving quadratic equations are explored, requiring students to apply both algebraic and (graphical methods - Unit 9) to find solutions. These concepts are reinforced through word problems that illustrate real-world applications, sharpening students' problem-solving skills and understanding of quadratic relationships.