Overview
This lecture introduces and illustrates quadratic equations for Grade 9 students, covering definitions, standard forms, and provides sample equations to recognize and construct quadratic equations.
Objectives of the Lesson
- Understand the definition of a quadratic equation.
- Identify the standard form of a quadratic equation.
- Distinguish quadratic equations from other types of equations.
- Provide examples of quadratic equations.
What is a Quadratic Equation?
- A quadratic equation is any equation that can be written in the form ax² + bx + c = 0 where a, b, and c are constants and a ≠ 0.
- The highest exponent of the variable (usually x) in a quadratic equation is always 2.
Standard Form
- Standard form of a quadratic equation: ax² + bx + c = 0.
- The coefficient a must not be zero for the equation to be quadratic.
Examples of Quadratic Equations
- x² = 9 can be rewritten as x² - 9 = 0; this is quadratic.
- 2x² + 3x - 5 = 0 is already in standard quadratic form.
- x(x - 2) = 10 expands to x² - 2x - 10 = 0, fitting the standard form.
- Quadratic equations may have missing terms (for example: x² - 4 = 0 has b = 0).
Non-Quadratic Equations
- Equations with x to the first power only (like 3x + 2 = 0) are linear, not quadratic.
- Equations with exponents higher than 2 (like x³ - 1 = 0) are not quadratic.
Key Terms & Definitions
- Quadratic Equation — an equation with the highest exponent of 2 for a variable, usually in the form ax² + bx + c = 0.
- Standard Form — the format ax² + bx + c = 0 for quadratic equations, with a ≠ 0.
- Coefficient — a number multiplying a variable in an equation.
- Constant — a fixed value in an equation (the c in ax² + bx + c).
Action Items / Next Steps
- Practice identifying and rewriting equations into quadratic standard form.
- Prepare for next lesson: Solving quadratic equations by extracting square roots.