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In the case of two parameters, the point describes a surface, called a parametric surface. In all cases, the equations are collectively called a parametric representation, [2] or parametric system, [3] or parameterization (also spelled parametrization, parametrisation) of the object. [1] [4] [5]
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features.
In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curves that have the formula: x y + a x 3 + b x 2 + c x = d {\displaystyle xy+ax^{3}+bx^{2}+cx=d}
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 ...
If x P = x Q, then there are two options: if y P = −y Q (case 3), including the case where y P = y Q = 0 (case 4), then the sum is defined as 0; thus, the inverse of each point on the curve is found by reflecting it across the x-axis. If y P = y Q ≠ 0, then Q = P and R = (x R, y R) = −(P + P) = −2P = −2Q (case 2 using P as R).
1.4 Curve families with variable genus. 2 Transcendental curves. ... Semicubical parabola. Serpentine curve. Trident curve. Trisectrix of Maclaurin. Tschirnhausen cubic.
The graph of a real single-variable quadratic function is a parabola. If a quadratic function is equated with zero, then the result is a quadratic equation . The solutions of a quadratic equation are the zeros (or roots ) of the corresponding quadratic function, of which there can be two, one, or zero.