Learn: Quadratic Equations

Welcome!Today we'll explore quadratic equations. These are equations where the highest power of the variable is 2. Let’s learn how to solve them step by step.

What is a Quadratic Equation?A quadratic equation is any equation of the form ax² + bx + c = 0, where a, b, and c are constants, and x is the variable. It’s important because quadratic equations model many real-world situations, such as projectile motion.

Standard Form of Quadratic EquationsThe standard form is written as ax² + bx + c = 0. Here, a, b, and c are numbers, and 'a' cannot be zero. Solving these helps us find the values of x that make the equation true.

Methods to Solve Quadratic EquationsThere are three main methods to solve quadratic equations: factorising, the quadratic formula, and completing the square. Let’s start with factorising.

FactorisingFactorising means rewriting the quadratic equation as a product of two brackets. For example, x² + 5x + 6 can be factorised into (x + 2)(x + 3). Setting each bracket equal to 0 gives the solutions.

The Quadratic FormulaIf factorising isn’t possible, we use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). This formula works for any quadratic equation.

Completing the SquareCompleting the square means rewriting the quadratic equation in the form (x + p)² = q. This method is useful for understanding the graph of the quadratic function and finding solutions.

Review Time!You’ve learned about quadratic equations, their standard form, and methods to solve them. Let’s test your understanding with a few questions.