Module 1: Introduction to Quadratic Equations
What is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree 2. The word "quadratic" comes from "quadratum," the Latin word for square, because the variable gets squared (like x²).
ax² + bx + c = 0
Where x represents an unknown, and a, b, and c are known numbers, with a ≠ 0.
Coefficient 'a'
Must not be zero. It determines how wide/narrow the parabola is and whether it opens up or down.
Coefficient 'b'
The linear coefficient. It shifts the axis of symmetry left or right.
Constant 'c'
The constant term. It represents the y-intercept of the graph.
Interactive Equation Builder
Adjust the values of a, b, and c to see how the equation changes.
Module 2: Factorization Method
Splitting the Middle Term
To factorize ax² + bx + c = 0, we find two numbers p and q such that:
- 1. p + q = b (Sum equals middle term)
- 2. p × q = a × c (Product equals outer terms)
Once split, we group terms and factor out common elements, applying the Zero-Product Rule: If A × B = 0, then A = 0 or B = 0.
Interactive Factorizer
Module 3: Completing the Square Method
This method transforms any quadratic equation into a perfect square trinomial form: (x + h)² = k.
Step-by-Step Algebra
Visual Representation
Visualizing x² + 6x forming a square.
Add (b/2)² to complete the square!
Module 4: Quadratic Formula Method
Discriminant & Roots
The term inside the square root, D = b² - 4ac, is called the Discriminant. It determines the nature of the roots:
- D > 0 Two distinct real roots.
- D = 0 Two equal real roots (one repeated).
- D < 0 No real roots (imaginary roots).
Live Calculator
Module 5: Graph of Quadratic Equation
The graph of y = ax² + bx + c is a curve called a Parabola.
Roots (x-ints): -2, 2
y-int: -4
Module 6: Numerical Problem Solver
Generate random quadratic problems and view step-by-step solutions.
Module 7: Verbal Word Problems
Quadratic equations model real-world situations like calculating areas, projectile motion, and optimal pricing.
Module 8: SEE Model Questions System
Practice integrated, context-based questions matching the new SEE examination pattern.
Module 9: Formula Reference
Standard Form
Conditions: a, b, c are real numbers, a ≠ 0.
Discriminant
Determines nature of roots. D>0 (Real, Distinct), D=0 (Real, Equal), D<0 (Imaginary).
Quadratic Formula
Universal method for finding roots.
Sum & Product of Roots
αβ = c/a
If roots α, β are given, equation is: x² - (α+β)x + αβ = 0.
Module 10: Interactive Quiz System
Test Your Knowledge!
30 High-Quality Questions covering all Quadratic Equation concepts.
- ⏱️ Timed Session
- 📊 Instant Feedback
- 🎓 SEE Grading System
Question Text
Module 11: Unlimited Practice Mode
Practice makes perfect. Generate endless mathematical questions.
Question
Module 12: Teacher & Student Dashboard
Student Performance Report
Quadratic Equation Lab - SEE Preparation
Quiz Attempts
Average Score
Highest Score
Attempt History
| # | Date & Time | Score | Accuracy | Grade |
|---|---|---|---|---|
| No quiz attempts yet. Go to Module 10! | ||||