Quadratic Functions

Quadratic Functions

Quadratic functions are polynomial functions of degree 2, typically written in the form f(x) = ax² + bx + c. They create parabolic curves when graphed and have many important applications.

Understanding Quadratic Functions

Learn the standard form, vertex form, and factored form of quadratic functions. Understand how each form reveals different information about the parabola.

Graphing Parabolas

Master techniques for graphing quadratic functions, including finding the vertex, axis of symmetry, y-intercept, and x-intercepts (roots).

Solving Quadratic Equations

Learn multiple methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula. Understand when each method is most appropriate.

The Discriminant

Understand how the discriminant (b² - 4ac) tells us about the nature of the roots: whether they are real or complex, and whether they are distinct or repeated.

Applications of Quadratic Functions

Explore real-world applications including projectile motion, optimization problems, and modeling situations where quadratic relationships exist.