We explore some geometric properties of these equations, in particular whether they have minimum or maximum values. Introduction One of the most popular real world applications of mathematics is that of curve fitting. Curve fitting involves examining what may seem like a random data set and deriving an equation that strongly describes that set. Functions commonly used for the purpose of curve fitting include exponential and logarithmic functions, but polynomial functions probably hold the most important role. In this paper, we will study quadratic curve fitting using systems of linear equations.
Quadratic Curve Fitting Perhaps the most fundamental polynomial is the quadratic equation.
The graph is in the shape of the letter u and is called a parabola. Definition 1 Let F be a fixed point and let l be a fixed line on the Cartesian plane. This hardly sounds like a description of a quadratic equation, but with simple geometry and algebraic manipulations we can show that it is. When investigating properties of parabolas, it is convenient to choose a directrix that is parallel to a vertical or a horizontal axis in the xy-plane. This we can do using rotation of axes.