![]() The process of completing the square results in a quadratic written in vertex form. ![]() This is where the “completing the square” process comes in. This point is useful for graphing the function, but it does not tell us where the graph will reach its maximum or minimum value. Quadratic equations are typically written in standard form, \(y=ax^2 bx c\), where c is a constant that identifies the y-intercept of the graph at (0, c). There are many applications that require the knowledge of where a function is at its maximum or minimum value, so being able to identify this point quickly is an important skill. If the function opens “down”, the vertex is the maximum point of the function, as if it were on the top of a hill. ![]() If the parabola opens “up”, the vertex is the minimum point of the function and can be visualized as the bottom of a valley. The vertex of a parabola is either the maximum or minimum value of the function. Graphs of quadratic functions are called parabolas. Before we attack the process, let’s review the basics of quadratic functions and their graphs. In this video, we will explore this process and work through some example problems to give you some practice.Īs mentioned, the process of completing the square allows us to identify the vertex of a quadratic, which is either the maximum or minimum value of the function. Specifically, completing the square helps us to identify the vertex of a quadratic graph and allows us to find the roots of a quadratic equation using the “square root” method. This algebraic process is important in the study of quadratic equations and their key features. Hi, and welcome to this video on the process of Completing the Square. ![]()
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