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The graph of the square function y = x 2 is a parabola. The squaring operation defines a real function called the square function or the squaring function. Its domain is the whole real line, and its image is the set of nonnegative real numbers. The square function preserves the order of positive numbers: larger numbers have larger squares.
In a Cartesian coordinate system with coordinates (x, y), a unit square is defined as a square consisting of the points where both x and y lie in a closed unit interval from 0 to 1. That is, a unit square is the Cartesian product I × I , where I denotes the closed unit interval.
Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x′,y′), where
For the quadratic function y = x 2 − x − 2, the points where the graph crosses the x-axis, x = −1 and x = 2, are the solutions of the quadratic equation x 2 − x − 2 = 0. The process of completing the square makes use of the algebraic identity x 2 + 2 h x + h 2 = ( x + h ) 2 , {\displaystyle x^{2}+2hx+h^{2}=(x+h)^{2},} which represents ...
The roots of the quadratic function y = 1 / 2 x 2 − 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.
These forbidden graphs are the cube (the simplex graph of K 3), the Cartesian product of an edge and a claw K 1,3 (the simplex graph of a claw), and the graphs formed from a gear graph by adding one more vertex connected to the hub of the wheel (the simplex graph of the disjoint union of a cycle with an isolated vertex).
Graph of y = ax 2 + bx + c, where a and the discriminant b 2 − 4ac are positive, with. Roots and y-intercept in red; Vertex and axis of symmetry in blue; Focus and directrix in pink; Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange).
An ordered pair of vertices, such as an edge in a directed graph. An arrow (x, y) has a tail x, a head y, and a direction from x to y; y is said to be the direct successor to x and x the direct predecessor to y. The arrow (y, x) is the inverted arrow of the arrow (x, y). articulation point A vertex in a connected graph whose removal would ...