IBDP Mathematics Analysis & Approaches HL Chapter 2 Notes

Functions Equations and Inequalities

STUDY NOTES FOR MATHEMATICS – CHAPTER 2 – Functions Equations and Inequalities

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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives

In this chapter we will study quadratic functions and investigate their graphs which are called parabolas. There are many examples of parabolas in everyday life, including water fountains, bridges and more. A quadratic function is a relationship between two variables x and y which can be written in the form y= ax^2+bx+c. This forms the basis of this chapter. We then use the discriminant. b^2- 4ac, to determine the number of real roots of the equation. If we are given sufficient information on or about a graph, we can also determine the quadratic in whatever form required. We then learn problem solving in quadratics and optimization with quadratics. Lastly, the chapter deals with quadratic inequalities and applying the quadratic formula.