Algebra 1 – Unit 9 – Quadratic Functions and Exponential Functions

Algebra 1 serves as a foundational course that introduces students to the essential concepts of quadratic and exponential functions, alongside their practical applications. Quadratic functions, represented by the standard form (y = ax^2 + bx + c), are pivotal in understanding parabolic graphs. Key properties such as vertex, axis of symmetry, and the direction of the parabola enable students to interpret and transform these graphs. Transformations, including shifts, reflections, and stretches, allow for a deeper comprehension of how changes in equations affect their graphical representations.

Furthermore, students explore exponential functions, characterized by equations of the form (y = ab^x), which model real-world scenarios such as population growth and radioactive decay. Understanding the nature of growth and decay is critical, as it applies to diverse fields like finance and biology. Additionally, recognizing geometric sequences as a form of exponential functions enriches students’ mathematical toolkit, empowering them to solve complex word problems. Mastery of these concepts equips learners with analytical skills essential for advanced mathematics and real-life problem-solving.