quadratic functions equations
Overview
This lesson introduces quadratic functions and equations, fundamental concepts in Pure Mathematics. We will explore their properties, various methods for solving quadratic equations, and how to interpret their graphs. Understanding quadratics is crucial for further topics in calculus and applied mathematics.
Introduction to Quadratic Functions and Equations
A **quadratic function** is defined by the general form f(x) = ax^2 + bx + c, where 'a', 'b', and 'c' are real constants and 'a' is not equal to zero. If 'a' were zero, the function would become linear. The graph of a quadratic function is a **parabola**, which is a symmetrical U-shaped curve. If 'a...
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Key Concepts
- Quadratic Function: A function of the form f(x) = ax^2 + bx + c, where a, b, c are constants and a is not equal to 0.
- Quadratic Equation: An equation of the form ax^2 + bx + c = 0, where a is not equal to 0.
- Roots of a Quadratic Equation: The values of x that satisfy the quadratic equation, also known as solutions or zeros.
- Vertex: The turning point of the parabola (the graph of a quadratic function), either a maximum or minimum point.
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Exam Tips
- →Always check the question for specific solution methods (e.g., 'by factorisation', 'by completing the square'). If not specified, use the most efficient method.
- →When using the quadratic formula, carefully substitute values for a, b, and c, paying close attention to signs, especially for 'b' and 'c'.
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