Chapter 2: Quadratics
This chapter delves into quadratic equations and their solutions, covering essential concepts for AS level pure maths algebraic expressions.
Definition: A quadratic equation is of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
The chapter outlines three main methods for solving quadratic equations:
- Factorization
- Completing the square
- Quadratic formula
Example: Completing the square for x² + 6x + 2:
x+3² - 9 + 2 = x+3² - 7
The quadratic formula is presented as:
x = −b±√(b2−4ac) / 2a
This chapter also introduces quadratic graphs, discussing their shape, key features, and how to find the turning point by completing the square.
Highlight: The direction of the parabola depends on the sign of 'a' in the quadratic equation ax² + bx + c.