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To convert the standard form to factored form, one needs only the quadratic formula to determine the two roots r 1 and r 2. To convert the standard form to vertex form, one needs a process called completing the square. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.
Animation depicting the process of completing the square. ( Details, animated GIF version) In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k . In other words, completing the square places a perfect square trinomial inside of a quadratic expression.
A 3-simplex, with barycentric subdivisions of 1-faces (edges) 2-faces (triangles) and 3-faces (body). In geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.).
To summarize: Any point in the projective plane is represented by a triple (X, Y, Z), called homogeneous coordinates or projective coordinates of the point, where X, Y and Z are not all 0. The point represented by a given set of homogeneous coordinates is unchanged if the coordinates are multiplied by a common factor.
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial ). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K.
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Trilinear coordinates. Small text. In geometry, the trilinear coordinates x : y : z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. Trilinear coordinates are an example of homogeneous coordinates. The ratio x : y is the ratio of the perpendicular distances from the point ...
Degree matrix. In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex —that is, the number of edges attached to each vertex. [ 1] It is used together with the adjacency matrix to construct the Laplacian matrix of a graph: the ...