Learn: Quadratic Equations

Welcome!Today we'll explore quadratic equations. These are essential for solving problems involving curves and have many applications in physics and engineering. Let's dive in!

What is a Quadratic Equation?A quadratic equation is a polynomial equation of degree 2, usually written as ax² + bx + c = 0, where a, b, and c are constants. The highest power of x is 2, making it quadratic.

Why are Quadratic Equations Important?Quadratic equations help us describe curves, such as the path of a thrown ball (parabola) or the shape of a satellite dish. They are widely used in science, engineering, and business.

Standard Form of Quadratic EquationThe standard form is ax² + bx + c = 0. Here, a is the coefficient of x², b is the coefficient of x, and c is the constant term. It's important to identify these values correctly for solving.

Solving Quadratic EquationsQuadratic equations can be solved using methods like factorisation, the quadratic formula, or completing the square. We'll focus on factorisation first.

Factorisation MethodFactorising means breaking the quadratic equation into two brackets, such as (x + p)(x + q) = 0. The values of p and q are chosen to satisfy the equation. This method works when the equation factors easily.

Quadratic FormulaWhen factorisation is difficult, use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. This formula works for all quadratic equations, even when they don't factorise easily.

Completing the SquareThis method rewrites the quadratic equation as a perfect square, making it easier to solve. For example, x² + 6x + 9 becomes (x + 3)² = 0.

Review Time!Well done! You've learned about quadratic equations, methods to solve them, and their importance. Let's review with some questions.