q quadratic equation
Answer (1)
Answer:A quadratic equation is a mathematical equation that can be written in the standard form: ax² + bx + c = 0 where: - a, b, and c are constants (numbers), and- x is the variable. Key Characteristics: - Highest Power: The highest power of the variable (x) in a quadratic equation is 2 (x²).- Three Terms: A quadratic equation typically has three terms: a squared term (ax²), a linear term (bx), and a constant term (c).- Parabola: When graphed, a quadratic equation creates a parabola, which is a symmetrical U-shaped curve. Examples: - 2x² + 5x - 3 = 0- x² - 4 = 0- 3x² + 7x = 0 Solving Quadratic Equations: There are several methods to solve quadratic equations, including: - Factoring: Breaking down the equation into two linear factors.- Quadratic Formula: A formula that directly provides the solutions.- Completing the Square: Transforming the equation into a perfect square trinomial. Applications: Quadratic equations are widely used in various fields, such as: - Physics: Modeling projectile motion, describing the path of a ball thrown in the air.- Engineering: Designing structures, calculating forces and stresses.- Finance: Calculating interest rates and investments.- Computer Science: Solving optimization problems.
