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Algebra 1 > Unit 2: Quadratic Functions

Solving Quadratic Equations: The Quadratic Formula

Lesson Content

[:::] 📘 HEADING
[:::] 📢 REAL-WORLD EXAMPLE

Let x = length, y = width

Area: xy = 24 → y = 24/x

Perimeter: 2x + 2y = 20

[:::] ∑️ EQUATION
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Where a, b, c are coefficients from ax² + bx + c = 0

[:::] 💡 WORKED EXAMPLE

Step 1: Identify a, b, c

a = 1, b = -5, c = 6

Step 2: Plug into formula

$$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(6)}}{2(1)}$$

Step 3: Simplify

x₁ = 3, x₂ = 2

[:::] 🎲 3D GEOMETRY
▲

Cone: r=5, h=10

Volume: 261.80 m³ • Surface Area: 254.16 m²

(Drag to rotate • Scroll to zoom)

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Algebra 1 › Unit 2 › Solving Quadratic Equations
Progress 75%

📘 Introduction to the Quadratic Formula

Estimated time: 15 min

📢

REAL-WORLD EXAMPLE

Building a Flower Garden 🌻

You want to build a rectangular flower garden with an area of 24 square meters. You have 20 meters of fencing. What should the dimensions be?

This real-world problem leads us to a quadratic equation!

∑️

THE QUADRATIC FORMULA

For any quadratic equation ax² + bx + c = 0:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

💡 The ± symbol means we get TWO solutions!

💡

WORKED EXAMPLE: Solving Step-by-Step

Problem: Solve x² - 5x + 6 = 0

Step 1 of 5: Identify the coefficients

a = 1 (coefficient of x²)

b = -5 (coefficient of x)

c = 6 (constant term)

🎮

INTERACTIVE: 3D Cone Visualization

▲

Volume: 261.80 m³ • Surface Area: 254.16 m²

(Drag to rotate • Scroll to zoom)

Table of Contents

✓ Introduction
✓ Real-World Example
✓ The Quadratic Formula
→ Worked Example
○ Practice Problems
○ Summary

Quick Practice Check

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Practice: Quadratic Equations

Question 3 of 5

Question 3

Solve the quadratic equation:

2x² - 8x + 6 = 0

Reference: Quadratic Formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Scratchpad

Class: Period 3 - Algebra 1

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⚠️ Below 70% mastery (5 students)

Student Avg Score Completion Last Active Action
Emma Wilson 58% 45% 2 days ago
Jake Thompson 62% 52% Today
Sofia Lee 68% 61% Yesterday

Most Difficult Questions

1. "Solve when discriminant = 0" 34% correct
2. "Word problems with quadratics" 41% correct
3. "Finding vertex from standard form" 47% correct