Search results
Results From The WOW.Com Content Network
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
() = + is called the vertex form, where h and k are the x and y coordinates of the vertex, respectively. The coefficient a is the same value in all three forms. To convert the standard form to factored form , one needs only the quadratic formula to determine the two roots r 1 and r 2 .
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.
Neighbourhood (graph theory) In this graph, the vertices adjacent to 5 are 1, 2 and 4. The neighbourhood of 5 is the graph consisting of the vertices 1, 2, 4 and the edge connecting 1 and 2. In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G is ...
Vertex (graph theory) A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a ...
That is, if a and b are homogeneous, one compares Y(a,z)Y(b,w) with εY(b,w)Y(a,z), where ε is –1 if both a and b are odd and 1 otherwise. If in addition there is a Virasoro element ω in the even part of V 2 , and the usual grading restrictions are satisfied, then V is called a vertex operator superalgebra .
A trirectangular tetrahedron can be constructed by a coordinate octant and a plane crossing all 3 axes away from the origin, like: x>0 y>0 z>0 and x/a+y/b+z/c<1. In geometry, a trirectangular tetrahedron is a tetrahedron where all three face angles at one vertex are right angles.