Unit 3: Quadratic Functions • Week 1

Introduction to Quadratic Functions

Discover parabolas, understand why they appear everywhere, and master the art of finding maximum and minimum values

NC Standards:NC.M1.F-IF.4NC.M1.F-IF.7NC.M1.A-SSE.1

Why This Matters

Anything with ACCELERATION (not just constant speed) is quadratic. Gravity makes things fall quadratically. Revenue often follows a parabola - price too low OR too high means less profit. Understanding quadratics helps you find the BEST point: maximum height, maximum profit, minimum cost.

The Big Idea

"Quadratics model situations with a BEST point (maximum or minimum). They have symmetry and a turning point called the vertex. The shape (parabola) appears everywhere in nature and business."

Real-World Connections

  • •Basketball shot: Height of ball vs time forms a parabola
  • •Business revenue: Often maximized at a specific price (not too low, not too high)
  • •Bridge design: Suspension bridges use parabolic cables
  • •Area problems: What dimensions give maximum area with limited perimeter?
  • •Physics: Any object thrown in the air follows a parabolic path

Common Misconceptions

  • ✗x² is just a rule to memorize → NO! It represents the AREA of a square with side x
  • ✗All parabolas look the same → NO! They can be wide, narrow, upward, or downward
  • ✗The vertex is always the maximum → NO! It can be a minimum if the parabola opens upward
  • ✗You only use quadratics in math class → NO! They appear in physics, economics, engineering, sports analytics...

💡 Before You Start: Ask Yourself

• What patterns do I notice?

• How does this connect to what I already know?

• Can I explain this in my own words?