2.2 Quadratic Equations and Functions

Solving quadratic equations, analyzing parabolas, and applying transformations to quadratic functions.

本节包含的知识点

• 2.2.1 Solving Quadratic Equations — Master multiple methods for solving quadratic equations including factoring, completing the square, quadratic formula, and graphical methods.
• 2.2.2 Parabola Properties and Graphs — Analyze the key features of parabolas such as vertex, axis of symmetry, focus, directrix, and direction of opening.
• 2.2.3 Quadratic Function Forms — Convert between standard form, vertex form, and factored form of quadratic functions and understand their geometric meanings.
• 2.2.4 Transformations of Quadratic Functions — Apply translations, reflections, and stretches to quadratic functions and understand how parameters affect the parabola.
• 2.2.5 Quadratic Inequalities — Solve quadratic inequalities and represent solutions using interval notation and number line graphs.
• 2.2.6 Applications and Modeling — Apply quadratic equations and functions to real-world problems such as projectile motion, optimization, and area problems.