Quadratic equations are second-degree polynomial equations that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants. They are called quadratic because the highest power of the variable is 2. Quadratic functions, on the other hand, are functions that can be represented by quadratic equations.

Quadratic equations and functions are essential in various areas, including physics, engineering, and finance. They often represent real-life situations such as the trajectory of a projectile, the behavior of populations, or the profit function of a business.

To better understand quadratic equations and functions, let's consider an example. Suppose we have a quadratic function f(x) = 2x^2 + 3x - 5. Here, the coefficient a is 2, b is 3, and c is -5. The graph of this function would be a downward-opening parabola. Quadratic equations can have zero, one, or two real solutions, which are the x-values where the graph intersects the x-axis.

In upcoming posts, we will explore various methods to solve quadratic equations, graph quadratic functions, and delve into real-life applications of these fundamental concepts. Stay tuned!