Contextualization
Theoretical Introduction
Quadratic functions represent a fundamental part of the study of polynomial functions in mathematics. They are characterized by the presence of an element squared, and a generic mathematical expression would be in the form: f(x) = ax² + bx + c, where a, b, and c are real constants and a is not equal to zero.
In the study of quadratic functions, there are concepts and terms that are essential for understanding them. These include the coefficient a that defines the opening of the parabola (graph of the 2nd degree function), the coefficient b which, together with a, defines the direction of the parabola's opening, and the coefficient c which defines where the parabola intersects the y-axis. In addition, we have the Delta (Δ), which determines the number of real roots that the function has.
Another central concept is the vertex of the parabola, which is the highest or lowest point of the parabola, depending on the direction of the opening. The study of quadratic functions involves understanding all these concepts and also knowing how to draw the parabola on the graph.
Contextualization
Quadratic functions have applications in various practical areas. In physics, for example, they are used to describe the motion of projectiles, where the height of the projectile is a function of time squared. In economics, quadratic functions also play an important role in cost-benefit analysis.
In the real world, quadratic functions are also essential for modeling situations involving growth and decay, such as the population of a species or the spread of a disease. Furthermore, in engineering and design, quadratic functions are used to model curves and shapes.
