Quadratic Functions | Precalculus (2026 Update) скачать в хорошем качестве

Quadratic Functions | Precalculus (2026 Update)

In Lesson 2.1 (Quadratic Functions) you’ll learn how to analyze and graph quadratic functions and connect the algebra to the graph. We cover: What makes a function quadratic and how it fits into the larger “polynomial family” Key graph features: opening direction, vertex, axis of symmetry, and minimum/maximum How to graph using vertex form and how to convert from standard form using completing the square A faster vertex method using x = −b / (2a), plus how to find x-intercepts by setting y = 0 A real-world application: finding the maximum height of a baseball using the vertex 🔗 Visit www.clopensets.com for full class videos, guided notes, and printable worksheets that go along with this lesson. 🔗 ClopenSets shop: https://www.etsy.com/shop/Clopensets #education #maths #math #highschoolmath #highschool Chapters 00:00 Intro: what we learn in Quadratic Functions 00:12 Polynomials & degree (linear vs quadratic vs higher) 00:59 Standard form of a quadratic: ax^2 + bx + c 01:07 Parent function & key characteristics 01:36 Opening up/down → min vs max (role of “a”) 02:10 Sketching quadratics from transformations (vertex form) 03:11 Standard form vs vertex form (important naming fix) 04:12 Converting standard → vertex form (two methods) 04:34 Method 1: Completing the square to find the vertex 07:23 Method 2: Axis of symmetry x = −b/(2a), then plug in 09:24 Finding x-intercepts (set y = 0 and solve) 10:30 Writing an equation in vertex form from vertex + point 12:16 Minimum/maximum occurs at the vertex 13:33 Application: baseball height → find maximum (vertex)